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Theorem outsideofcol 35782
Description: Outside of implies colinearity. (Contributed by Scott Fenton, 26-Oct-2013.) (Revised by Mario Carneiro, 19-Apr-2014.)
Assertion
Ref Expression
outsideofcol (𝑃OutsideOfβŸ¨π‘„, π‘…βŸ© β†’ 𝑃 Colinear βŸ¨π‘„, π‘…βŸ©)

Proof of Theorem outsideofcol
StepHypRef Expression
1 broutsideof 35770 . 2 (𝑃OutsideOfβŸ¨π‘„, π‘…βŸ© ↔ (𝑃 Colinear βŸ¨π‘„, π‘…βŸ© ∧ Β¬ 𝑃 Btwn βŸ¨π‘„, π‘…βŸ©))
21simplbi 496 1 (𝑃OutsideOfβŸ¨π‘„, π‘…βŸ© β†’ 𝑃 Colinear βŸ¨π‘„, π‘…βŸ©)
Colors of variables: wff setvar class
Syntax hints:  Β¬ wn 3   β†’ wi 4  βŸ¨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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