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Theorem outsideofcol 25975
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 25963 . 2  |-  ( POutsideOf <. Q ,  R >.  <->  ( P  Colinear  <. Q ,  R >.  /\  -.  P  Btwn  <. Q ,  R >. ) )
21simplbi 447 1  |-  ( POutsideOf <. Q ,  R >.  ->  P  Colinear  <. Q ,  R >. )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   <.cop 3781   class class class wbr 4176    Btwn cbtwn 25736    Colinear ccolin 25879  OutsideOfcoutsideof 25961
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1552  ax-5 1563  ax-17 1623  ax-9 1662  ax-8 1683  ax-6 1740  ax-7 1745  ax-11 1757  ax-12 1946  ax-ext 2389
This theorem depends on definitions:  df-bi 178  df-an 361  df-tru 1325  df-ex 1548  df-nf 1551  df-sb 1656  df-clab 2395  df-cleq 2401  df-clel 2404  df-nfc 2533  df-v 2922  df-dif 3287  df-br 4177  df-outsideof 25962
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