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Theorem outsideofcol 31203
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 31191 . 2 (𝑃OutsideOf⟨𝑄, 𝑅⟩ ↔ (𝑃 Colinear ⟨𝑄, 𝑅⟩ ∧ ¬ 𝑃 Btwn ⟨𝑄, 𝑅⟩))
21simplbi 474 1 (𝑃OutsideOf⟨𝑄, 𝑅⟩ → 𝑃 Colinear ⟨𝑄, 𝑅⟩)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  cop 4130   class class class wbr 4577   Btwn cbtwn 25514   Colinear ccolin 31107  OutsideOfcoutsideof 31189
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1712  ax-4 1727  ax-5 1826  ax-6 1874  ax-7 1921  ax-10 2005  ax-11 2020  ax-12 2033  ax-13 2233  ax-ext 2589
This theorem depends on definitions:  df-bi 195  df-or 383  df-an 384  df-tru 1477  df-ex 1695  df-nf 1700  df-sb 1867  df-clab 2596  df-cleq 2602  df-clel 2605  df-nfc 2739  df-v 3174  df-dif 3542  df-br 4578  df-outsideof 31190
This theorem is referenced by: (None)
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