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Theorem cbvopab2v 4527
 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 4220 . . . . . . 7
21eqeq2d 2481 . . . . . 6
3 cbvopab2v.1 . . . . . 6
42, 3anbi12d 710 . . . . 5
54cbvexv 1997 . . . 4
65exbii 1644 . . 3
76abbii 2601 . 2
8 df-opab 4512 . 2
9 df-opab 4512 . 2
107, 8, 93eqtr4i 2506 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1379  wex 1596  cab 2452  cop 4039  copab 4510 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1382  df-ex 1597  df-nf 1600  df-sb 1712  df-clab 2453  df-cleq 2459  df-clel 2462  df-nfc 2617  df-rab 2826  df-v 3120  df-dif 3484  df-un 3486  df-in 3488  df-ss 3495  df-nul 3791  df-if 3946  df-sn 4034  df-pr 4036  df-op 4040  df-opab 4512 This theorem is referenced by: (None)
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