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Theorem outsideofcol 24828
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 24816 . 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 3656   class class class wbr 4039    Btwn cbtwn 24589    Colinear ccolin 24732  OutsideOfcoutsideof 24814
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-dif 3168  df-br 4040  df-outsideof 24815
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