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Theorem cnvopab 5412
Description: The converse of a class abstraction of ordered pairs. (Contributed by NM, 11-Dec-2003.) (Proof shortened by Andrew Salmon, 27-Aug-2011.)
Assertion
Ref Expression
cnvopab
Distinct variable group:   ,

Proof of Theorem cnvopab
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 relcnv 5379 . 2
2 relopab 5134 . 2
3 opelopabsbALT 4761 . . . 4
4 sbcom2 2189 . . . 4
53, 4bitri 249 . . 3
6 vex 3112 . . . 4
7 vex 3112 . . . 4
86, 7opelcnv 5189 . . 3
9 opelopabsbALT 4761 . . 3
105, 8, 93bitr4i 277 . 2
111, 2, 10eqrelriiv 5102 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  [wsb 1739  e.wcel 1818  <.cop 4035  {copab 4509  `'ccnv 5003
This theorem is referenced by:  mptcnv  5413  cnvxp  5429  mptpreima  5505  f1ocnvd  6524  mapsncnv  7485  compsscnv  8772  xkocnv  20315  lgsquadlem3  23631  axcontlem2  24268  cnvadj  26811  f1o3d  27471  cnvoprab  27546  dfiso2  32568
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-br 4453  df-opab 4511  df-xp 5010  df-rel 5011  df-cnv 5012
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