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Theorem outsideofcol 26072
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 26060 . 2  |-  ( POutsideOf <. Q ,  R >.  <->  ( P  Colinear  <. Q ,  R >.  /\  -.  P  Btwn  <. Q ,  R >. ) )
21simplbi 448 1  |-  ( POutsideOf <. Q ,  R >.  ->  P  Colinear  <. Q ,  R >. )
Colors of variables: wff set class
Syntax hints:   -. wn 3    -> wi 4   <.cop 3819   class class class wbr 4215    Btwn cbtwn 25833    Colinear ccolin 25976  OutsideOfcoutsideof 26058
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-dif 3325  df-br 4216  df-outsideof 26059
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