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Theorem cnvopab 5236
 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:   ,
Allowed substitution hints:   (,)

Proof of Theorem cnvopab
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 relcnv 5206 . 2
2 relopab 4959 . 2
3 opelopabsbALT 4709 . . . 4
4 sbcom2 2273 . . . 4
53, 4bitri 253 . . 3
6 vex 3047 . . . 4
7 vex 3047 . . . 4
86, 7opelcnv 5015 . . 3
9 opelopabsbALT 4709 . . 3
105, 8, 93bitr4i 281 . 2
111, 2, 10eqrelriiv 4928 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1443  wsb 1796   wcel 1886  cop 3973  copab 4459  ccnv 4832 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-9 1895  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430  ax-sep 4524  ax-nul 4533  ax-pr 4638 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 986  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-eu 2302  df-mo 2303  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ne 2623  df-ral 2741  df-rex 2742  df-rab 2745  df-v 3046  df-dif 3406  df-un 3408  df-in 3410  df-ss 3417  df-nul 3731  df-if 3881  df-sn 3968  df-pr 3970  df-op 3974  df-br 4402  df-opab 4461  df-xp 4839  df-rel 4840  df-cnv 4841 This theorem is referenced by:  mptcnv  5237  cnvxp  5253  mptpreima  5327  f1ocnvd  6515  mapsncnv  7515  compsscnv  8798  dfiso2  15670  xkocnv  20822  lgsquadlem3  24277  axcontlem2  24988  cnvadj  27538  f1o3d  28222  cnvoprab  28301
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