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Theorem cbvoprab1 6368
 Description: Rule used to change first bound variable in an operation abstraction, using implicit substitution. (Contributed by NM, 20-Dec-2008.) (Revised by Mario Carneiro, 5-Dec-2016.)
Hypotheses
Ref Expression
cbvoprab1.1
cbvoprab1.2
cbvoprab1.3
Assertion
Ref Expression
cbvoprab1
Distinct variable group:   ,,,
Allowed substitution hints:   (,,,)   (,,,)

Proof of Theorem cbvoprab1
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1708 . . . . . 6
2 cbvoprab1.1 . . . . . 6
31, 2nfan 1929 . . . . 5
43nfex 1949 . . . 4
5 nfv 1708 . . . . . 6
6 cbvoprab1.2 . . . . . 6
75, 6nfan 1929 . . . . 5
87nfex 1949 . . . 4
9 opeq1 4219 . . . . . . 7
109eqeq2d 2471 . . . . . 6
11 cbvoprab1.3 . . . . . 6
1210, 11anbi12d 710 . . . . 5
1312exbidv 1715 . . . 4
144, 8, 13cbvex 2023 . . 3
1514opabbii 4521 . 2
16 dfoprab2 6342 . 2
17 dfoprab2 6342 . 2
1815, 16, 173eqtr4i 2496 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1395  wex 1613  wnf 1617  cop 4038  copab 4514  coprab 6297 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1619  ax-4 1632  ax-5 1705  ax-6 1748  ax-7 1791  ax-9 1823  ax-10 1838  ax-11 1843  ax-12 1855  ax-13 2000  ax-ext 2435  ax-sep 4578  ax-nul 4586  ax-pr 4695 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1614  df-nf 1618  df-sb 1741  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-rab 2816  df-v 3111  df-dif 3474  df-un 3476  df-in 3478  df-ss 3485  df-nul 3794  df-if 3945  df-sn 4033  df-pr 4035  df-op 4039  df-opab 4516  df-oprab 6300 This theorem is referenced by: (None)
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