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Theorem dmopab 4546
 Description: The domain of a class of ordered pairs. (Contributed by NM, 16-May-1995.) (Revised by Mario Carneiro, 4-Dec-2016.)
Assertion
Ref Expression
dmopab
Distinct variable group:   ,
Allowed substitution hints:   (,)

Proof of Theorem dmopab
StepHypRef Expression
1 nfopab1 3826 . . 3
2 nfopab2 3827 . . 3
31, 2dfdmf 4528 . 2
4 df-br 3765 . . . . 5
5 opabid 3994 . . . . 5
64, 5bitri 173 . . . 4
76exbii 1496 . . 3
87abbii 2153 . 2
93, 8eqtri 2060 1
 Colors of variables: wff set class Syntax hints:   wceq 1243  wex 1381   wcel 1393  cab 2026  cop 3378   class class class wbr 3764  copab 3817   cdm 4345 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-14 1405  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-sep 3875  ax-pow 3927  ax-pr 3944 This theorem depends on definitions:  df-bi 110  df-3an 887  df-tru 1246  df-nf 1350  df-sb 1646  df-eu 1903  df-mo 1904  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559  df-un 2922  df-in 2924  df-ss 2931  df-pw 3361  df-sn 3381  df-pr 3382  df-op 3384  df-br 3765  df-opab 3819  df-dm 4355 This theorem is referenced by:  dmopabss  4547  dmopab3  4548  fndmin  5274  dmoprab  5585  shftdm  9423
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