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Mirrors > Home > MPE Home > Th. List > Mathboxes > outsideofcol | Structured version Visualization version GIF version |
Description: Outside of implies colinearity. (Contributed by Scott Fenton, 26-Oct-2013.) (Revised by Mario Carneiro, 19-Apr-2014.) |
Ref | Expression |
---|---|
outsideofcol | β’ (πOutsideOfβ¨π, π β© β π Colinear β¨π, π β©) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | broutsideof 35770 | . 2 β’ (πOutsideOfβ¨π, π β© β (π Colinear β¨π, π β© β§ Β¬ π Btwn β¨π, π β©)) | |
2 | 1 | simplbi 496 | 1 β’ (πOutsideOfβ¨π, π β© β π Colinear β¨π, π β©) |
Colors of variables: wff setvar class |
Syntax hints: Β¬ wn 3 β wi 4 β¨cop 4631 class class class wbr 5144 Btwn cbtwn 28739 Colinear ccolin 35686 OutsideOfcoutsideof 35768 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1789 ax-4 1803 ax-5 1905 ax-6 1963 ax-7 2003 ax-8 2100 ax-9 2108 ax-ext 2696 |
This theorem depends on definitions: df-bi 206 df-an 395 df-tru 1536 df-ex 1774 df-sb 2060 df-clab 2703 df-cleq 2717 df-clel 2802 df-v 3465 df-dif 3944 df-br 5145 df-outsideof 35769 |
This theorem is referenced by: (None) |
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