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Theorem dfoprab4pop 25037
 Description: Class abstraction for operations in terms of class abstraction of ordered pairs. (A version of dfoprab4 6177 adapted to partial operations.) (Contributed by FL, 18-Apr-2010.)
Hypothesis
Ref Expression
dfoprab4pop.1
Assertion
Ref Expression
dfoprab4pop
Distinct variable groups:   ,,,,   ,,   ,
Allowed substitution hints:   (,)   (,,)

Proof of Theorem dfoprab4pop
StepHypRef Expression
1 elrel 4789 . . . . . . 7
21adantrr 697 . . . . . 6
32ex 423 . . . . 5
43pm4.71rd 616 . . . 4
5 19.41vv 1843 . . . . 5
6 eleq1 2343 . . . . . . . 8
7 dfoprab4pop.1 . . . . . . . 8
86, 7anbi12d 691 . . . . . . 7
98pm5.32i 618 . . . . . 6
1092exbii 1570 . . . . 5
115, 10bitr3i 242 . . . 4
124, 11syl6bb 252 . . 3
1312opabbidv 4082 . 2
14 dfoprab2 5895 . 2
1513, 14syl6eqr 2333 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176   wa 358  wex 1528   wceq 1623   wcel 1684  cop 3643  copab 4076   wrel 4694  coprab 5859 This theorem is referenced by:  fnovpop  25038 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-14 1688  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264  ax-sep 4141  ax-nul 4149  ax-pr 4214 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-3an 936  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-ne 2448  df-rab 2552  df-v 2790  df-dif 3155  df-un 3157  df-in 3159  df-ss 3166  df-nul 3456  df-if 3566  df-sn 3646  df-pr 3647  df-op 3649  df-opab 4078  df-xp 4695  df-rel 4696  df-oprab 5862
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