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Theorem opabbi2dv 4598
 Description: Deduce equality of a relation and an ordered-pair class builder. Compare abbi2dv 2207. (Contributed by NM, 24-Feb-2014.)
Hypotheses
Ref Expression
opabbi2dv.1
opabbi2dv.3
Assertion
Ref Expression
opabbi2dv
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,)

Proof of Theorem opabbi2dv
StepHypRef Expression
1 opabbi2dv.1 . . 3
2 opabid2 4580 . . 3
31, 2ax-mp 7 . 2
4 opabbi2dv.3 . . 3
54opabbidv 3910 . 2
63, 5syl5eqr 2135 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1290   wcel 1439  cop 3453  copab 3904   wrel 4457 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 666  ax-5 1382  ax-7 1383  ax-gen 1384  ax-ie1 1428  ax-ie2 1429  ax-8 1441  ax-10 1442  ax-11 1443  ax-i12 1444  ax-bndl 1445  ax-4 1446  ax-14 1451  ax-17 1465  ax-i9 1469  ax-ial 1473  ax-i5r 1474  ax-ext 2071  ax-sep 3963  ax-pow 4015  ax-pr 4045 This theorem depends on definitions:  df-bi 116  df-3an 927  df-tru 1293  df-nf 1396  df-sb 1694  df-eu 1952  df-mo 1953  df-clab 2076  df-cleq 2082  df-clel 2085  df-nfc 2218  df-ral 2365  df-rex 2366  df-v 2622  df-un 3004  df-in 3006  df-ss 3013  df-pw 3435  df-sn 3456  df-pr 3457  df-op 3459  df-opab 3906  df-xp 4458  df-rel 4459 This theorem is referenced by: (None)
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