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Theorem opelopab2a 4048
 Description: Ordered pair membership in an ordered pair class abstraction. (Contributed by Mario Carneiro, 19-Dec-2013.)
Hypothesis
Ref Expression
opelopabga.1
Assertion
Ref Expression
opelopab2a
Distinct variable groups:   ,,   ,,   ,,   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem opelopab2a
StepHypRef Expression
1 eleq1 2145 . . . . 5
2 eleq1 2145 . . . . 5
31, 2bi2anan9 571 . . . 4
4 opelopabga.1 . . . 4
53, 4anbi12d 457 . . 3
65opelopabga 4046 . 2
76bianabs 576 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103   wceq 1285   wcel 1434  cop 3419  copab 3858 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-14 1446  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-sep 3916  ax-pow 3968  ax-pr 3992 This theorem depends on definitions:  df-bi 115  df-3an 922  df-tru 1288  df-nf 1391  df-sb 1688  df-eu 1946  df-mo 1947  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-un 2986  df-in 2988  df-ss 2995  df-pw 3402  df-sn 3422  df-pr 3423  df-op 3425  df-opab 3860 This theorem is referenced by:  opelopab2  4053  brab2a  4439  brab2ga  4461  ltdfpr  6810
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