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Theorem opabdm 28058
 Description: Domain of an ordered-pair class abstraction. (Contributed by Thierry Arnoux, 31-Aug-2017.)
Assertion
Ref Expression
opabdm
Distinct variable group:   ,,
Allowed substitution hints:   (,)

Proof of Theorem opabdm
StepHypRef Expression
1 df-dm 4864 . 2
2 nfopab1 4492 . . . 4
32nfeq2 2608 . . 3
4 nfopab2 4493 . . . . 5
54nfeq2 2608 . . . 4
6 df-br 4427 . . . . 5
7 eleq2 2502 . . . . . 6
8 opabid 4728 . . . . . 6
97, 8syl6bb 264 . . . . 5
106, 9syl5bb 260 . . . 4
115, 10exbid 1939 . . 3
123, 11abbid 2564 . 2
131, 12syl5eq 2482 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wceq 1437  wex 1659   wcel 1870  cab 2414  cop 4008   class class class wbr 4426  copab 4483   cdm 4854 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 1751  ax-6 1797  ax-7 1841  ax-9 1874  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407  ax-sep 4548  ax-nul 4556  ax-pr 4661 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 1790  df-eu 2270  df-mo 2271  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2579  df-ne 2627  df-rab 2791  df-v 3089  df-dif 3445  df-un 3447  df-in 3449  df-ss 3456  df-nul 3768  df-if 3916  df-sn 4003  df-pr 4005  df-op 4009  df-br 4427  df-opab 4485  df-dm 4864 This theorem is referenced by:  fpwrelmapffslem  28160
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