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Theorem cbvopab2v 4283
 Description: Rule used to change the second bound variable in an ordered pair abstraction, using implicit substitution. (Contributed by NM, 2-Sep-1999.)
Hypothesis
Ref Expression
cbvopab2v.1
Assertion
Ref Expression
cbvopab2v
Distinct variable groups:   ,,   ,   ,
Allowed substitution hints:   (,)   (,)

Proof of Theorem cbvopab2v
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 opeq2 3986 . . . . . . 7
21eqeq2d 2448 . . . . . 6
3 cbvopab2v.1 . . . . . 6
42, 3anbi12d 693 . . . . 5
54cbvexv 1986 . . . 4
65exbii 1593 . . 3
76abbii 2549 . 2
8 df-opab 4268 . 2
9 df-opab 4268 . 2
107, 8, 93eqtr4i 2467 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 178   wa 360  wex 1551   wceq 1653  cab 2423  cop 3818  copab 4266 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-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418 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-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  df-opab 4268
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