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Theorem opelopab4 28575
 Description: Ordered pair membership in a class abstraction of pairs. Compare to elopab 4454. (Contributed by Alan Sare, 8-Feb-2014.) (Revised by Mario Carneiro, 6-May-2015.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
opelopab4
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)

Proof of Theorem opelopab4
StepHypRef Expression
1 elopab 4454 . 2
2 vex 2951 . . . . . 6
3 vex 2951 . . . . . 6
42, 3opth 4427 . . . . 5
5 eqcom 2437 . . . . 5
64, 5bitr3i 243 . . . 4
76anbi1i 677 . . 3
872exbii 1593 . 2
91, 8bitr4i 244 1
 Colors of variables: wff set class Syntax hints:   wb 177   wa 359  wex 1550   wceq 1652   wcel 1725  cop 3809  copab 4257 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-3an 938  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-ne 2600  df-rab 2706  df-v 2950  df-dif 3315  df-un 3317  df-in 3319  df-ss 3326  df-nul 3621  df-if 3732  df-sn 3812  df-pr 3813  df-op 3815  df-opab 4259
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