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Theorem opabid2 5137
 Description: A relation expressed as an ordered pair abstraction. (Contributed by NM, 11-Dec-2006.)
Assertion
Ref Expression
opabid2
Distinct variable group:   ,,

Proof of Theorem opabid2
Dummy variables are mutually distinct and distinct from all other variables.
StepHypRef Expression
1 vex 3112 . . . 4
2 vex 3112 . . . 4
3 opeq1 4217 . . . . 5
43eleq1d 2526 . . . 4
5 opeq2 4218 . . . . 5
65eleq1d 2526 . . . 4
71, 2, 4, 6opelopab 4774 . . 3
87gen2 1619 . 2
9 relopab 5134 . . 3
10 eqrel 5097 . . 3
119, 10mpan 670 . 2
128, 11mpbiri 233 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  e.wcel 1818  <.cop 4035  {copab 4509  Relwrel 5009 This theorem is referenced by:  opabbi2dv  5157 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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