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Theorem colinrel 30836
 Description: Colinearity is a relationship. (Contributed by Scott Fenton, 7-Nov-2013.) (Revised by Mario Carneiro, 19-Apr-2014.)
Assertion
Ref Expression
colinrel

Proof of Theorem colinrel
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 relcnv 5210 . 2
2 df-colinear 30818 . . 3
32releqi 4921 . 2
41, 3mpbir 213 1
 Colors of variables: wff setvar class Syntax hints:   wa 371   w3o 985   w3a 986   wcel 1889  wrex 2740  cop 3976   class class class wbr 4405  ccnv 4836   wrel 4842  cfv 5585  coprab 6296  cn 10616  cee 24930   cbtwn 24931   ccolin 30816 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1671  ax-4 1684  ax-5 1760  ax-6 1807  ax-7 1853  ax-9 1898  ax-10 1917  ax-11 1922  ax-12 1935  ax-13 2093  ax-ext 2433  ax-sep 4528  ax-nul 4537  ax-pr 4642 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 988  df-tru 1449  df-ex 1666  df-nf 1670  df-sb 1800  df-clab 2440  df-cleq 2446  df-clel 2449  df-nfc 2583  df-ne 2626  df-ral 2744  df-rex 2745  df-rab 2748  df-v 3049  df-dif 3409  df-un 3411  df-in 3413  df-ss 3420  df-nul 3734  df-if 3884  df-sn 3971  df-pr 3973  df-op 3977  df-opab 4465  df-xp 4843  df-rel 4844  df-cnv 4845  df-colinear 30818 This theorem is referenced by:  brcolinear2  30837
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