Predicate Logic Proof Example 3 Using Universal Instantiation
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=uLu8ihQz510
An example of a predicate logic proof that illustrates the use of Universal Instantiation.","styleRuns":[{"startIndex":0,"length":90,"styleRunExtensions":{"styleRunColorMapExtension":{"colorMap":[{"key":"USER_INTERFACE_THEME_DARK","value":4294967295},{"key":"USER_INTERFACE_THEME_LIGHT","value":4279440147}]}},"fontFamilyName":"Roboto"}]},"headerRuns":[{"startIndex":0,"length":90,"headerMapping":"ATTRIBUTED_STRING_HEADER_MAPPING_UNSPECIFIED"}]}},{"itemSectionRenderer":{"contents":[{"continuationItemRenderer":{"trigger":"CONTINUATION_TRIGGER_ON_ITEM_SHOWN","continuationEndpoint":{"clickTrackingParams":"CMQBELsvGAIiEwic0suU4MuLAxWK00IFHXj4Cwc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/next"}},"continuationCommand":{"token":"Eg0SC3VMdThpaFF6NTEwGAYyJSIRIgt1THU4aWhRejUxMDAAeAJCEGNvbW1lbnRzLXNlY3Rpb24%3D","request":"CONTINUATION_REQUEST_TYPE_WATCH_NEXT"}}}}],"trackingParams":"CMQBELsvGAIiEwic0suU4MuLAxWK00IFHXj4Cwc=","sectionIdentifier":"comment-item-section","targetId":"comments-section"}}],"trackingParams":"CMMBELovIhMInNLLlODLiwMVitNCBR14-AsH"}},"secondaryResults":{"secondaryResults":{"results":[{"compactVideoRenderer":{"videoId":"BfZ1EU3daxs","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/BfZ1EU3daxs/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLCVnrCtGUyGu_i5CoYVJTeaqHYZdA","width":168,"height":94},{"url":"https://i.ytimg.com/vi/BfZ1EU3daxs/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLAP8spGLex4rKlZ5Agcs4708skyKA","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Predicate Logic Proof Example 5: Existential Instantiation and Generalization by FREGE: A Logic Course Elaine Rich, Alan Cline 7,078 views 9 years ago 5 minutes, 33 seconds"}},"simpleText":"Predicate Logic Proof Example 5: Existential Instantiation and Generalization"},"longBylineText":{"runs":[{"text":"FREGE: A Logic Course Elaine Rich, Alan Cline","navigationEndpoint":{"clickTrackingParams":"CLwBEKQwGAAiEwic0suU4MuLAxWK00IFHXj4CwcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@fregealogiccourseelaineric4905","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC6nzXqWHi1UhZdKGcyhuOSw","canonicalBaseUrl":"/@fregealogiccourseelaineric4905"}}}]},"publishedTimeText":{"simpleText":"9 years ago"},"viewCountText":{"simpleText":"7,078 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"5 minutes, 33 seconds"}},"simpleText":"5:33"},"navigationEndpoint":{"clickTrackingParams":"CLwBEKQwGAAiEwic0suU4MuLAxWK00IFHXj4CwcyB3JlbGF0ZWRI3c7PoaGR7924AZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=BfZ1EU3daxs","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"BfZ1EU3daxs","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=05f675114ddd6b1b ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1816250 mt=1739830862 oweuc= pxtags=Cg4KAnR4Egg1MTM4ODU0NA rxtags=Cg4KAnR4Egg1MTM4ODU0Mg%2CCg4KAnR4Egg1MTM4ODU0Mw%2CCg4KAnR4Egg1MTM4ODU0NA%2CCg4KAnR4Egg1MTM4ODU0NQ"}}}}},"shortBylineText":{"runs":[{"text":"FREGE: A Logic Course Elaine Rich, Alan Cline","navigationEndpoint":{"clickTrackingParams":"CLwBEKQwGAAiEwic0suU4MuLAxWK00IFHXj4CwcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@fregealogiccourseelaineric4905","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC6nzXqWHi1UhZdKGcyhuOSw","canonicalBaseUrl":"/@fregealogiccourseelaineric4905"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_nAkRZAgBf0_fA2k87MEk3fchbVLekAM8iDpZEckfo=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CLwBEKQwGAAiEwic0suU4MuLAxWK00IFHXj4CwdAm9b17pSinfsF","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"7K views"}},"simpleText":"7K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CMEBEP6YBBgFIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CMEBEP6YBBgFIhMInNLLlODLiwMVitNCBR14-AsH","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"BfZ1EU3daxs","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CMEBEP6YBBgFIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["BfZ1EU3daxs"],"params":"CAQ%3D"}},"videoIds":["BfZ1EU3daxs"]}},{"clickTrackingParams":"CMEBEP6YBBgFIhMInNLLlODLiwMVitNCBR14-AsH","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CMIBELlqIhMInNLLlODLiwMVitNCBR14-AsH"}},"popupType":"TOAST"}}]}},"trackingParams":"CMEBEP6YBBgFIhMInNLLlODLiwMVitNCBR14-AsH"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CMABENGqBRgGIhMInNLLlODLiwMVitNCBR14-AsH","offlineVideoEndpoint":{"videoId":"BfZ1EU3daxs","onAddCommand":{"clickTrackingParams":"CMABENGqBRgGIhMInNLLlODLiwMVitNCBR14-AsH","getDownloadActionCommand":{"videoId":"BfZ1EU3daxs","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CMABENGqBRgGIhMInNLLlODLiwMVitNCBR14-AsH"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLwBEKQwGAAiEwic0suU4MuLAxWK00IFHXj4Cwc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtCZloxRVUzZGF4cw%3D%3D","commands":[{"clickTrackingParams":"CLwBEKQwGAAiEwic0suU4MuLAxWK00IFHXj4Cwc=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CL8BEI5iIhMInNLLlODLiwMVitNCBR14-AsH","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLwBEKQwGAAiEwic0suU4MuLAxWK00IFHXj4Cwc=","hasSeparator":true}}],"trackingParams":"CLwBEKQwGAAiEwic0suU4MuLAxWK00IFHXj4Cwc=","accessibility":{"accessibilityData":{"label":"Action menu"}},"targetId":"watch-related-menu-button"}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"5 minutes, 33 seconds"}},"simpleText":"5:33"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CL4BEPnnAxgBIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"BfZ1EU3daxs","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CL4BEPnnAxgBIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"BfZ1EU3daxs"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CL4BEPnnAxgBIhMInNLLlODLiwMVitNCBR14-AsH"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CL0BEMfsBBgCIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CL0BEMfsBBgCIhMInNLLlODLiwMVitNCBR14-AsH","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"BfZ1EU3daxs","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CL0BEMfsBBgCIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["BfZ1EU3daxs"],"params":"CAQ%3D"}},"videoIds":["BfZ1EU3daxs"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CL0BEMfsBBgCIhMInNLLlODLiwMVitNCBR14-AsH"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Predicate Logic Proof Example 5: Existential Instantiation and Generalization - 5 minutes, 33 seconds - Go to channel - FREGE: A Logic Course Elaine Rich, Alan Cline - 7K views - 9 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"GJpezCUMOxA","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/GJpezCUMOxA/hqdefault.jpg?sqp=-oaymwE1CKgBEF5IVfKriqkDKAgBFQAAiEIYAXABwAEG8AEB-AH-CYAC0AWKAgwIABABGGUgZShlMA8= rs=AOn4CLBbnobfGM4m7k7gCJgalTUw1MVvaw","width":168,"height":94},{"url":"https://i.ytimg.com/vi/GJpezCUMOxA/hqdefault.jpg?sqp=-oaymwE2CNACELwBSFXyq4qpAygIARUAAIhCGAFwAcABBvABAfgB_gmAAtAFigIMCAAQARhlIGUoZTAP rs=AOn4CLCjbi-cvMR6hhBO0v8GLkO9OVHx8g","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Universal and Existential Quantifiers, ∀ For All and ∃ There Exists by Dr. Trefor Bazett 370,324 views 7 years ago 9 minutes, 32 seconds"}},"simpleText":"Universal and Existential Quantifiers, ∀ For All and ∃ There Exists "},"longBylineText":{"runs":[{"text":"Dr. Trefor Bazett","navigationEndpoint":{"clickTrackingParams":"CLUBEKQwGAEiEwic0suU4MuLAxWK00IFHXj4CwcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@DrTrefor","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC9rTsvTxJnx1DNrDA3Rqa6A","canonicalBaseUrl":"/@DrTrefor"}}}]},"publishedTimeText":{"simpleText":"7 years ago"},"viewCountText":{"simpleText":"370,324 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"9 minutes, 32 seconds"}},"simpleText":"9:32"},"navigationEndpoint":{"clickTrackingParams":"CLUBEKQwGAEiEwic0suU4MuLAxWK00IFHXj4CwcyB3JlbGF0ZWRI3c7PoaGR7924AZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=GJpezCUMOxA","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"GJpezCUMOxA","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-uxaxiv0nxx5q-nv4l.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=189a5ecc250c3b10 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1033750 mt=1739830862 oweuc= pxtags=Cg4KAnR4Egg1MTM4ODU0NA rxtags=Cg4KAnR4Egg1MTM4ODU0Mg%2CCg4KAnR4Egg1MTM4ODU0Mw%2CCg4KAnR4Egg1MTM4ODU0NA%2CCg4KAnR4Egg1MTM4ODU0NQ"}}}}},"shortBylineText":{"runs":[{"text":"Dr. Trefor Bazett","navigationEndpoint":{"clickTrackingParams":"CLUBEKQwGAEiEwic0suU4MuLAxWK00IFHXj4CwcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@DrTrefor","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC9rTsvTxJnx1DNrDA3Rqa6A","canonicalBaseUrl":"/@DrTrefor"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_lAOi_1eAO-NKrsecIaYKpj05qQlLen6MFoxZv0kp-NWw=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"ownerBadges":[{"metadataBadgeRenderer":{"icon":{"iconType":"CHECK_CIRCLE_THICK"},"style":"BADGE_STYLE_TYPE_VERIFIED","tooltip":"Verified","trackingParams":"CLUBEKQwGAEiEwic0suU4MuLAxWK00IFHXj4Cwc=","accessibilityData":{"label":"Verified"}}}],"trackingParams":"CLUBEKQwGAEiEwic0suU4MuLAxWK00IFHXj4CwdAkPawqMLZl80Y","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"370K views"}},"simpleText":"370K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CLoBEP6YBBgHIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLoBEP6YBBgHIhMInNLLlODLiwMVitNCBR14-AsH","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"GJpezCUMOxA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLoBEP6YBBgHIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["GJpezCUMOxA"],"params":"CAQ%3D"}},"videoIds":["GJpezCUMOxA"]}},{"clickTrackingParams":"CLoBEP6YBBgHIhMInNLLlODLiwMVitNCBR14-AsH","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CLsBELlqIhMInNLLlODLiwMVitNCBR14-AsH"}},"popupType":"TOAST"}}]}},"trackingParams":"CLoBEP6YBBgHIhMInNLLlODLiwMVitNCBR14-AsH"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CLkBENGqBRgIIhMInNLLlODLiwMVitNCBR14-AsH","offlineVideoEndpoint":{"videoId":"GJpezCUMOxA","onAddCommand":{"clickTrackingParams":"CLkBENGqBRgIIhMInNLLlODLiwMVitNCBR14-AsH","getDownloadActionCommand":{"videoId":"GJpezCUMOxA","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CLkBENGqBRgIIhMInNLLlODLiwMVitNCBR14-AsH"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CLUBEKQwGAEiEwic0suU4MuLAxWK00IFHXj4Cwc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtHSnBlekNVTU94QQ%3D%3D","commands":[{"clickTrackingParams":"CLUBEKQwGAEiEwic0suU4MuLAxWK00IFHXj4Cwc=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CLgBEI5iIhMInNLLlODLiwMVitNCBR14-AsH","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CLUBEKQwGAEiEwic0suU4MuLAxWK00IFHXj4Cwc=","hasSeparator":true}}],"trackingParams":"CLUBEKQwGAEiEwic0suU4MuLAxWK00IFHXj4Cwc=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"9 minutes, 32 seconds"}},"simpleText":"9:32"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLcBEPnnAxgCIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"GJpezCUMOxA","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CLcBEPnnAxgCIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"GJpezCUMOxA"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLcBEPnnAxgCIhMInNLLlODLiwMVitNCBR14-AsH"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLYBEMfsBBgDIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLYBEMfsBBgDIhMInNLLlODLiwMVitNCBR14-AsH","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"GJpezCUMOxA","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLYBEMfsBBgDIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["GJpezCUMOxA"],"params":"CAQ%3D"}},"videoIds":["GJpezCUMOxA"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLYBEMfsBBgDIhMInNLLlODLiwMVitNCBR14-AsH"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Universal and Existential Quantifiers, ∀ For All and ∃ There Exists - 9 minutes, 32 seconds - Go to channel - Dr. Trefor Bazett - 370K views - 7 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/GJpezCUMOxA/mqdefault_6s.webp?du=3000 sqp=CIDezr0G rs=AOn4CLBAnJcaa6CyDUpF-OoWziqvRbfVAQ","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"oaSLa1Ya5-M","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/oaSLa1Ya5-M/hqdefault.jpg?sqp=-oaymwEbCKgBEF5IVfKriqkDDggBFQAAiEIYAXABwAEG rs=AOn4CLBboyrwCWyAG7irffN1nma8mk6YMg","width":168,"height":94},{"url":"https://i.ytimg.com/vi/oaSLa1Ya5-M/hqdefault.jpg?sqp=-oaymwEcCNACELwBSFXyq4qpAw4IARUAAIhCGAFwAcABBg== rs=AOn4CLCD7n_7PsgKM_2gerlr6aBXwJ3-4w","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Law of the Excluded Middle - Part 1 by FREGE: A Logic Course Elaine Rich, Alan Cline 25,371 views 9 years ago 5 minutes, 27 seconds"}},"simpleText":"Law of the Excluded Middle - Part 1"},"longBylineText":{"runs":[{"text":"FREGE: A Logic Course Elaine Rich, Alan Cline","navigationEndpoint":{"clickTrackingParams":"CK4BEKQwGAIiEwic0suU4MuLAxWK00IFHXj4CwcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@fregealogiccourseelaineric4905","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC6nzXqWHi1UhZdKGcyhuOSw","canonicalBaseUrl":"/@fregealogiccourseelaineric4905"}}}]},"publishedTimeText":{"simpleText":"9 years ago"},"viewCountText":{"simpleText":"25,371 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"5 minutes, 27 seconds"}},"simpleText":"5:27"},"navigationEndpoint":{"clickTrackingParams":"CK4BEKQwGAIiEwic0suU4MuLAxWK00IFHXj4CwcyB3JlbGF0ZWRI3c7PoaGR7924AZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=oaSLa1Ya5-M","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"oaSLa1Ya5-M","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr1---sn-nv47lnsd.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=a1a48b6b561ae7e3 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1833750 mt=1739830862 oweuc= pxtags=Cg4KAnR4Egg1MTM4ODU0NA rxtags=Cg4KAnR4Egg1MTM4ODU0Mg%2CCg4KAnR4Egg1MTM4ODU0Mw%2CCg4KAnR4Egg1MTM4ODU0NA%2CCg4KAnR4Egg1MTM4ODU0NQ"}}}}},"shortBylineText":{"runs":[{"text":"FREGE: A Logic Course Elaine Rich, Alan Cline","navigationEndpoint":{"clickTrackingParams":"CK4BEKQwGAIiEwic0suU4MuLAxWK00IFHXj4CwcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@fregealogiccourseelaineric4905","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC6nzXqWHi1UhZdKGcyhuOSw","canonicalBaseUrl":"/@fregealogiccourseelaineric4905"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_nAkRZAgBf0_fA2k87MEk3fchbVLekAM8iDpZEckfo=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CK4BEKQwGAIiEwic0suU4MuLAxWK00IFHXj4CwdA48_rsLXtotKhAQ==","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"25K views"}},"simpleText":"25K views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CLMBEP6YBBgGIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CLMBEP6YBBgGIhMInNLLlODLiwMVitNCBR14-AsH","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"oaSLa1Ya5-M","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CLMBEP6YBBgGIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["oaSLa1Ya5-M"],"params":"CAQ%3D"}},"videoIds":["oaSLa1Ya5-M"]}},{"clickTrackingParams":"CLMBEP6YBBgGIhMInNLLlODLiwMVitNCBR14-AsH","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CLQBELlqIhMInNLLlODLiwMVitNCBR14-AsH"}},"popupType":"TOAST"}}]}},"trackingParams":"CLMBEP6YBBgGIhMInNLLlODLiwMVitNCBR14-AsH"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CLIBENGqBRgHIhMInNLLlODLiwMVitNCBR14-AsH","offlineVideoEndpoint":{"videoId":"oaSLa1Ya5-M","onAddCommand":{"clickTrackingParams":"CLIBENGqBRgHIhMInNLLlODLiwMVitNCBR14-AsH","getDownloadActionCommand":{"videoId":"oaSLa1Ya5-M","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CLIBENGqBRgHIhMInNLLlODLiwMVitNCBR14-AsH"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CK4BEKQwGAIiEwic0suU4MuLAxWK00IFHXj4Cwc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtvYVNMYTFZYTUtTQ%3D%3D","commands":[{"clickTrackingParams":"CK4BEKQwGAIiEwic0suU4MuLAxWK00IFHXj4Cwc=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CLEBEI5iIhMInNLLlODLiwMVitNCBR14-AsH","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CK4BEKQwGAIiEwic0suU4MuLAxWK00IFHXj4Cwc=","hasSeparator":true}}],"trackingParams":"CK4BEKQwGAIiEwic0suU4MuLAxWK00IFHXj4Cwc=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"5 minutes, 27 seconds"}},"simpleText":"5:27"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CLABEPnnAxgBIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"oaSLa1Ya5-M","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CLABEPnnAxgBIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"oaSLa1Ya5-M"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CLABEPnnAxgBIhMInNLLlODLiwMVitNCBR14-AsH"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CK8BEMfsBBgCIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CK8BEMfsBBgCIhMInNLLlODLiwMVitNCBR14-AsH","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"oaSLa1Ya5-M","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CK8BEMfsBBgCIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["oaSLa1Ya5-M"],"params":"CAQ%3D"}},"videoIds":["oaSLa1Ya5-M"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CK8BEMfsBBgCIhMInNLLlODLiwMVitNCBR14-AsH"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Law of the Excluded Middle - Part 1 - 5 minutes, 27 seconds - Go to channel - FREGE: A Logic Course Elaine Rich, Alan Cline - 25K views - 9 years ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/oaSLa1Ya5-M/mqdefault_6s.webp?du=3000 sqp=CIq8zr0G rs=AOn4CLBmgQY6E156Idr886gaCY5ZTh-F8A","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"compactVideoRenderer":{"videoId":"RfSGkkkGtPg","thumbnail":{"thumbnails":[{"url":"https://i.ytimg.com/vi/RfSGkkkGtPg/hqdefault.jpg?sqp=-oaymwE1CKgBEF5IVfKriqkDKAgBFQAAiEIYAXABwAEG8AEB-AH-CYAC0AWKAgwIABABGGUgYChNMA8= rs=AOn4CLBPXILTou0pqJaE7uBYsQjly0EJ8Q","width":168,"height":94},{"url":"https://i.ytimg.com/vi/RfSGkkkGtPg/hqdefault.jpg?sqp=-oaymwE2CNACELwBSFXyq4qpAygIARUAAIhCGAFwAcABBvABAfgB_gmAAtAFigIMCAAQARhlIGAoTTAP rs=AOn4CLCbrUveky5K2jSK7oUEWBsDwbd76Q","width":336,"height":188}]},"title":{"accessibility":{"accessibilityData":{"label":"Proof in predicate logic 1: Universal Instantiation by Simon Cushing 437 views 1 year ago 17 minutes"}},"simpleText":"Proof in predicate logic 1: Universal Instantiation"},"longBylineText":{"runs":[{"text":"Simon Cushing","navigationEndpoint":{"clickTrackingParams":"CKcBEKQwGAMiEwic0suU4MuLAxWK00IFHXj4CwcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@SimonCushing","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC7ctu5bxvqyF759_54mHSyw","canonicalBaseUrl":"/@SimonCushing"}}}]},"publishedTimeText":{"simpleText":"1 year ago"},"viewCountText":{"simpleText":"437 views"},"lengthText":{"accessibility":{"accessibilityData":{"label":"17 minutes, 10 seconds"}},"simpleText":"17:10"},"navigationEndpoint":{"clickTrackingParams":"CKcBEKQwGAMiEwic0suU4MuLAxWK00IFHXj4CwcyB3JlbGF0ZWRI3c7PoaGR7924AZoBBQgBEPgd","commandMetadata":{"webCommandMetadata":{"url":"/watch?v=RfSGkkkGtPg","webPageType":"WEB_PAGE_TYPE_WATCH","rootVe":3832}},"watchEndpoint":{"videoId":"RfSGkkkGtPg","nofollow":true,"watchEndpointSupportedOnesieConfig":{"html5PlaybackOnesieConfig":{"commonConfig":{"url":"https://rr4---sn-nvm-cxbz.googlevideo.com/initplayback?source=youtube oeis=1 c=WEB oad=3200 ovd=3200 oaad=11000 oavd=11000 ocs=700 oewis=1 oputc=1 ofpcc=1 msp=1 odepv=1 onvi=1 id=45f486924906b4f8 ip=2a02%3A27aa%3A0%3A0%3A0%3A0%3A0%3Ad49 initcwndbps=1816250 mt=1739830862 oweuc= pxtags=Cg4KAnR4Egg1MTM4ODU0NA rxtags=Cg4KAnR4Egg1MTM4ODU0Mg%2CCg4KAnR4Egg1MTM4ODU0Mw%2CCg4KAnR4Egg1MTM4ODU0NA%2CCg4KAnR4Egg1MTM4ODU0NQ"}}}}},"shortBylineText":{"runs":[{"text":"Simon Cushing","navigationEndpoint":{"clickTrackingParams":"CKcBEKQwGAMiEwic0suU4MuLAxWK00IFHXj4CwcyB3JlbGF0ZWQ=","commandMetadata":{"webCommandMetadata":{"url":"/@SimonCushing","webPageType":"WEB_PAGE_TYPE_CHANNEL","rootVe":3611,"apiUrl":"/youtubei/v1/browse"}},"browseEndpoint":{"browseId":"UC7ctu5bxvqyF759_54mHSyw","canonicalBaseUrl":"/@SimonCushing"}}}]},"channelThumbnail":{"thumbnails":[{"url":"https://yt3.ggpht.com/ytc/AIdro_kSNoOvBbH8ttanpP2dQrasZU3hcNBL8h0Gtx2sTw0zggs=s68-c-k-c0x00ffffff-no-rj","width":68,"height":68}]},"trackingParams":"CKcBEKQwGAMiEwic0suU4MuLAxWK00IFHXj4CwdA-OmayKTSofpF","shortViewCountText":{"accessibility":{"accessibilityData":{"label":"437 views"}},"simpleText":"437 views"},"menu":{"menuRenderer":{"items":[{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Add to queue"}]},"icon":{"iconType":"ADD_TO_QUEUE_TAIL"},"serviceEndpoint":{"clickTrackingParams":"CKwBEP6YBBgGIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKwBEP6YBBgGIhMInNLLlODLiwMVitNCBR14-AsH","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"RfSGkkkGtPg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKwBEP6YBBgGIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["RfSGkkkGtPg"],"params":"CAQ%3D"}},"videoIds":["RfSGkkkGtPg"]}},{"clickTrackingParams":"CKwBEP6YBBgGIhMInNLLlODLiwMVitNCBR14-AsH","openPopupAction":{"popup":{"notificationActionRenderer":{"responseText":{"simpleText":"Added to queue"},"trackingParams":"CK0BELlqIhMInNLLlODLiwMVitNCBR14-AsH"}},"popupType":"TOAST"}}]}},"trackingParams":"CKwBEP6YBBgGIhMInNLLlODLiwMVitNCBR14-AsH"}},{"menuServiceItemDownloadRenderer":{"serviceEndpoint":{"clickTrackingParams":"CKsBENGqBRgHIhMInNLLlODLiwMVitNCBR14-AsH","offlineVideoEndpoint":{"videoId":"RfSGkkkGtPg","onAddCommand":{"clickTrackingParams":"CKsBENGqBRgHIhMInNLLlODLiwMVitNCBR14-AsH","getDownloadActionCommand":{"videoId":"RfSGkkkGtPg","params":"CAIQAA%3D%3D"}}}},"trackingParams":"CKsBENGqBRgHIhMInNLLlODLiwMVitNCBR14-AsH"}},{"menuServiceItemRenderer":{"text":{"runs":[{"text":"Share"}]},"icon":{"iconType":"SHARE"},"serviceEndpoint":{"clickTrackingParams":"CKcBEKQwGAMiEwic0suU4MuLAxWK00IFHXj4Cwc=","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/share/get_share_panel"}},"shareEntityServiceEndpoint":{"serializedShareEntity":"CgtSZlNHa2trR3RQZw%3D%3D","commands":[{"clickTrackingParams":"CKcBEKQwGAMiEwic0suU4MuLAxWK00IFHXj4Cwc=","openPopupAction":{"popup":{"unifiedSharePanelRenderer":{"trackingParams":"CKoBEI5iIhMInNLLlODLiwMVitNCBR14-AsH","showLoadingSpinner":true}},"popupType":"DIALOG","beReused":true}}]}},"trackingParams":"CKcBEKQwGAMiEwic0suU4MuLAxWK00IFHXj4Cwc=","hasSeparator":true}}],"trackingParams":"CKcBEKQwGAMiEwic0suU4MuLAxWK00IFHXj4Cwc=","accessibility":{"accessibilityData":{"label":"Action menu"}}}},"thumbnailOverlays":[{"thumbnailOverlayTimeStatusRenderer":{"text":{"accessibility":{"accessibilityData":{"label":"17 minutes, 10 seconds"}},"simpleText":"17:10"},"style":"DEFAULT"}},{"thumbnailOverlayToggleButtonRenderer":{"isToggled":false,"untoggledIcon":{"iconType":"WATCH_LATER"},"toggledIcon":{"iconType":"CHECK"},"untoggledTooltip":"Watch later","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKkBEPnnAxgBIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"addedVideoId":"RfSGkkkGtPg","action":"ACTION_ADD_VIDEO"}]}},"toggledServiceEndpoint":{"clickTrackingParams":"CKkBEPnnAxgBIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/browse/edit_playlist"}},"playlistEditEndpoint":{"playlistId":"WL","actions":[{"action":"ACTION_REMOVE_VIDEO_BY_VIDEO_ID","removedVideoId":"RfSGkkkGtPg"}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Watch later"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKkBEPnnAxgBIhMInNLLlODLiwMVitNCBR14-AsH"}},{"thumbnailOverlayToggleButtonRenderer":{"untoggledIcon":{"iconType":"ADD_TO_QUEUE_TAIL"},"toggledIcon":{"iconType":"PLAYLIST_ADD_CHECK"},"untoggledTooltip":"Add to queue","toggledTooltip":"Added","untoggledServiceEndpoint":{"clickTrackingParams":"CKgBEMfsBBgCIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true}},"signalServiceEndpoint":{"signal":"CLIENT_SIGNAL","actions":[{"clickTrackingParams":"CKgBEMfsBBgCIhMInNLLlODLiwMVitNCBR14-AsH","addToPlaylistCommand":{"openMiniplayer":false,"openListPanel":true,"videoId":"RfSGkkkGtPg","listType":"PLAYLIST_EDIT_LIST_TYPE_QUEUE","onCreateListCommand":{"clickTrackingParams":"CKgBEMfsBBgCIhMInNLLlODLiwMVitNCBR14-AsH","commandMetadata":{"webCommandMetadata":{"sendPost":true,"apiUrl":"/youtubei/v1/playlist/create"}},"createPlaylistServiceEndpoint":{"videoIds":["RfSGkkkGtPg"],"params":"CAQ%3D"}},"videoIds":["RfSGkkkGtPg"]}}]}},"untoggledAccessibility":{"accessibilityData":{"label":"Add to queue"}},"toggledAccessibility":{"accessibilityData":{"label":"Added"}},"trackingParams":"CKgBEMfsBBgCIhMInNLLlODLiwMVitNCBR14-AsH"}},{"thumbnailOverlayNowPlayingRenderer":{"text":{"runs":[{"text":"Now playing"}]}}}],"accessibility":{"accessibilityData":{"label":"Proof in predicate logic 1: Universal Instantiation - 17 minutes - Go to channel - Simon Cushing - 437 views - 1 year ago - play video"}},"richThumbnail":{"movingThumbnailRenderer":{"movingThumbnailDetails":{"thumbnails":[{"url":"https://i.ytimg.com/an_webp/RfSGkkkGtPg/mqdefault_6s.webp?du=3000 sqp=CIi0zr0G rs=AOn4CLCUp3ZFdKuxeWPJbOPjozBAqWY2HA","width":320,"height":180}],"logAsMovingThumbnail":true},"enableHoveredLogging":true,"enableOverlay":true}}}},{"lockupViewModel":{"contentImage":{"collectionThumbnailViewModel":{"primaryThumbnail":{"thumbnailViewModel":{"image":{"sources":[{"url":"https://i.ytimg.com/vi/A3Ffwsnad0k/hqdefault.jpg?sqp=-oaymwEWCKgBEF5IWvKriqkDCQgBFQAAiEIYAQ== rs=AOn4CLCNimnPqvvSEUuQ4j8ieJE-tk8bMQ","width":168,"height":94},{"url":"https://i.ytimg.com/vi/A3Ffwsnad0k/hqdefault.jpg?sqp=-oaymwEXCNACELwBSFryq4qpAwkIARUAAIhCGAE= rs=AOn4CLDtQN1fnxbq65UZo-tuqUNr5ewVMA","width":336,"height":188}]},"overlays":[{"thumbnailOverlayBadgeViewModel":{"thumbnailBadges":[{"thumbnailBadgeViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAYLISTS"}}]},"text":"80 videos","badgeStyle":"THUMBNAIL_OVERLAY_BADGE_STYLE_DEFAULT","backgroundColor":{"lightTheme":3355443,"darkTheme":3355443}}}],"position":"THUMBNAIL_OVERLAY_BADGE_POSITION_BOTTOM_END"}},{"thumbnailHoverOverlayViewModel":{"icon":{"sources":[{"clientResource":{"imageName":"PLAY_ALL"}}]},"text":{"content":"Play all","styleRuns":[{"startIndex":0,"length":8}]},"style":"THUMBNAIL_HOVER_OVERLAY_STYLE_COVER"}}],"backgroundColor":{"lightTheme":4144959,"darkTheme":4144959}}},"stackColor":{"lightTheme":10066329,"darkTheme":9211020}}},"metadata":{"lockupMetadataViewModel":{"title":{"content":"Discrete Math I (Entire Course)"},"metadata":{"contentMetadataViewModel":{"metadataRows":[{"metadataParts":[{"text":{"content":"Kimberly Brehm
#############################
![](http://youtor.org/essay_main.png)