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Theorem outsideofcol 33702
 Description: Outside of implies colinearity. (Contributed by Scott Fenton, 26-Oct-2013.) (Revised by Mario Carneiro, 19-Apr-2014.)
Assertion
Ref Expression
outsideofcol (𝑃OutsideOf⟨𝑄, 𝑅⟩ → 𝑃 Colinear ⟨𝑄, 𝑅⟩)

Proof of Theorem outsideofcol
StepHypRef Expression
1 broutsideof 33690 . 2 (𝑃OutsideOf⟨𝑄, 𝑅⟩ ↔ (𝑃 Colinear ⟨𝑄, 𝑅⟩ ∧ ¬ 𝑃 Btwn ⟨𝑄, 𝑅⟩))
21simplbi 501 1 (𝑃OutsideOf⟨𝑄, 𝑅⟩ → 𝑃 Colinear ⟨𝑄, 𝑅⟩)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4  ⟨cop 4534   class class class wbr 5033   Btwn cbtwn 26686   Colinear ccolin 33606  OutsideOfcoutsideof 33688 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2114  ax-9 2122  ax-ext 2773 This theorem depends on definitions:  df-bi 210  df-an 400  df-ex 1782  df-sb 2070  df-clab 2780  df-cleq 2794  df-clel 2873  df-v 3446  df-dif 3887  df-br 5034  df-outsideof 33689 This theorem is referenced by: (None)
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