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Theorem colinearperm3 30401
 Description: Permutation law for colinearity. Part of theorem 4.11 of [Schwabhauser] p. 36. (Contributed by Scott Fenton, 5-Oct-2013.)
Assertion
Ref Expression
colinearperm3

Proof of Theorem colinearperm3
StepHypRef Expression
1 3orrot 980 . . 3
21a1i 11 . 2
3 brcolinear 30397 . 2
4 3anrot 979 . . 3
5 brcolinear 30397 . . 3
64, 5sylan2b 473 . 2
72, 3, 63bitr4d 285 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 367   w3o 973   w3a 974   wcel 1842  cop 3978   class class class wbr 4395  cfv 5569  cn 10576  cee 24608   cbtwn 24609   ccolin 30375 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-9 1846  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380  ax-sep 4517  ax-nul 4525  ax-pr 4630 This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-3or 975  df-3an 976  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-eu 2242  df-mo 2243  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-ne 2600  df-ral 2759  df-rex 2760  df-rab 2763  df-v 3061  df-dif 3417  df-un 3419  df-in 3421  df-ss 3428  df-nul 3739  df-if 3886  df-sn 3973  df-pr 3975  df-op 3979  df-uni 4192  df-br 4396  df-opab 4454  df-xp 4829  df-rel 4830  df-cnv 4831  df-iota 5533  df-fv 5577  df-oprab 6282  df-colinear 30377 This theorem is referenced by:  colinearperm2  30402  colinearperm4  30403  btwncolinear4  30410
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