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Theorem outsideofcol 24756
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 24744 . 2  |-  ( POutsideOf <. Q ,  R >.  <->  ( P  Colinear  <. Q ,  R >.  /\  -.  P  Btwn  <. Q ,  R >. ) )
21simplbi 446 1  |-  ( POutsideOf <. Q ,  R >.  ->  P  Colinear  <. Q ,  R >. )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   <.cop 3643   class class class wbr 4023    Btwn cbtwn 24517    Colinear ccolin 24660  OutsideOfcoutsideof 24742
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-dif 3155  df-br 4024  df-outsideof 24743
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