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Theorem dmopab 5218
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:   ,

Proof of Theorem dmopab
StepHypRef Expression
1 nfopab1 4518 . . 3
2 nfopab2 4519 . . 3
31, 2dfdmf 5201 . 2
4 df-br 4453 . . . . 5
5 opabid 4759 . . . . 5
64, 5bitri 249 . . . 4
76exbii 1667 . . 3
87abbii 2591 . 2
93, 8eqtri 2486 1
Colors of variables: wff setvar class
Syntax hints:  =wceq 1395  E.wex 1612  e.wcel 1818  {cab 2442  <.cop 4035   class class class wbr 4452  {copab 4509  domcdm 5004
This theorem is referenced by:  dmopabss  5219  dmopab3  5220  opabiotadm  5935  fndmin  5994  dmoprab  6383  zfrep6  6768  hartogslem1  7988  rankf  8233  dfac3  8523  axdc2lem  8849  shftdm  12904  adjeu  26808  mptfnf  27499  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-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-dm 5014
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