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Theorem copsex4g 4446
 Description: An implicit substitution inference for 2 ordered pairs. (Contributed by NM, 5-Aug-1995.)
Hypothesis
Ref Expression
copsex4g.1
Assertion
Ref Expression
copsex4g
Distinct variable groups:   ,,,,   ,,,,   ,,,,   ,,,,   ,,,,   ,,,,   ,,,,
Allowed substitution hints:   (,,,)

Proof of Theorem copsex4g
StepHypRef Expression
1 eqcom 2439 . . . . . . 7
2 vex 2960 . . . . . . . 8
3 vex 2960 . . . . . . . 8
42, 3opth 4436 . . . . . . 7
51, 4bitri 242 . . . . . 6
6 eqcom 2439 . . . . . . 7
7 vex 2960 . . . . . . . 8
8 vex 2960 . . . . . . . 8
97, 8opth 4436 . . . . . . 7
106, 9bitri 242 . . . . . 6
115, 10anbi12i 680 . . . . 5
1211anbi1i 678 . . . 4
1312a1i 11 . . 3
14134exbidv 1641 . 2
15 id 21 . . 3
16 copsex4g.1 . . 3
1715, 16cgsex4g 2990 . 2
1814, 17bitrd 246 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wex 1551   wceq 1653   wcel 1726  cop 3818 This theorem is referenced by:  opbrop  4956  ov3  6211 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-14 1730  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418  ax-sep 4331  ax-nul 4339  ax-pr 4404 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-3an 939  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-ne 2602  df-rab 2715  df-v 2959  df-dif 3324  df-un 3326  df-in 3328  df-ss 3335  df-nul 3630  df-if 3741  df-sn 3821  df-pr 3822  df-op 3824
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