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Theorem opabbi2dv 5157
 Description: Deduce equality of a relation and an ordered-pair class builder. Compare abbi2dv 2594. (Contributed by NM, 24-Feb-2014.)
Hypotheses
Ref Expression
opabbi2dv.1
opabbi2dv.3
Assertion
Ref Expression
opabbi2dv
Distinct variable groups:   ,,   ,,

Proof of Theorem opabbi2dv
StepHypRef Expression
1 opabbi2dv.1 . . 3
2 opabid2 5137 . . 3
31, 2ax-mp 5 . 2
4 opabbi2dv.3 . . 3
54opabbidv 4515 . 2
63, 5syl5eqr 2512 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  e.wcel 1818  <.cop 4035  {copab 4509  Relwrel 5009 This theorem is referenced by:  recmulnq  9363  dib1dim  36892 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-9 1822  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-sep 4573  ax-nul 4581  ax-pr 4691 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-eu 2286  df-mo 2287  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-rex 2813  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511  df-xp 5010  df-rel 5011
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