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Theorem dmopab 5056
 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 4483 . . 3
2 nfopab2 4484 . . 3
31, 2dfdmf 5039 . 2
4 df-br 4418 . . . . 5
5 opabid 4719 . . . . 5
64, 5bitri 252 . . . 4
76exbii 1712 . . 3
87abbii 2554 . 2
93, 8eqtri 2449 1
 Colors of variables: wff setvar class Syntax hints:   wceq 1437  wex 1659   wcel 1867  cab 2405  cop 3999   class class class wbr 4417  copab 4474   cdm 4845 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1838  ax-9 1871  ax-10 1886  ax-11 1891  ax-12 1904  ax-13 2052  ax-ext 2398  ax-sep 4539  ax-nul 4547  ax-pr 4652 This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-3an 984  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-eu 2267  df-mo 2268  df-clab 2406  df-cleq 2412  df-clel 2415  df-nfc 2570  df-ne 2618  df-rab 2782  df-v 3080  df-dif 3436  df-un 3438  df-in 3440  df-ss 3447  df-nul 3759  df-if 3907  df-sn 3994  df-pr 3996  df-op 4000  df-br 4418  df-opab 4476  df-dm 4855 This theorem is referenced by:  dmopabss  5057  dmopab3  5058  mptfnf  5708  opabiotadm  5934  fndmin  5995  dmoprab  6382  zfrep6  6766  hartogslem1  8048  rankf  8255  dfac3  8541  axdc2lem  8867  shftdm  13102  dfiso2  15621  adjeu  27403
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