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Theorem outsideofcol 30971
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 30959 . 2  |-  ( POutsideOf <. Q ,  R >.  <->  ( P  Colinear  <. Q ,  R >.  /\  -.  P  Btwn  <. Q ,  R >. ) )
21simplbi 467 1  |-  ( POutsideOf <. Q ,  R >.  ->  P  Colinear  <. Q ,  R >. )
Colors of variables: wff setvar class
Syntax hints:   -. wn 3    -> wi 4   <.cop 3965   class class class wbr 4395    Btwn cbtwn 24998    Colinear ccolin 30875  OutsideOfcoutsideof 30957
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1677  ax-4 1690  ax-5 1766  ax-6 1813  ax-7 1859  ax-10 1932  ax-11 1937  ax-12 1950  ax-13 2104  ax-ext 2451
This theorem depends on definitions:  df-bi 190  df-an 378  df-tru 1455  df-ex 1672  df-nf 1676  df-sb 1806  df-clab 2458  df-cleq 2464  df-clel 2467  df-nfc 2601  df-v 3033  df-dif 3393  df-br 4396  df-outsideof 30958
This theorem is referenced by: (None)
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