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Theorem cbvoprab2 6137
 Description: Change the second bound variable in an operation abstraction. (Contributed by Jeff Madsen, 11-Jun-2010.) (Revised by Mario Carneiro, 11-Dec-2016.)
Hypotheses
Ref Expression
cbvoprab2.1
cbvoprab2.2
cbvoprab2.3
Assertion
Ref Expression
cbvoprab2
Distinct variable group:   ,,,
Allowed substitution hints:   (,,,)   (,,,)

Proof of Theorem cbvoprab2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1629 . . . . . . 7
2 cbvoprab2.1 . . . . . . 7
31, 2nfan 1846 . . . . . 6
43nfex 1865 . . . . 5
5 nfv 1629 . . . . . . 7
6 cbvoprab2.2 . . . . . . 7
75, 6nfan 1846 . . . . . 6
87nfex 1865 . . . . 5
9 opeq2 3977 . . . . . . . . 9
109opeq1d 3982 . . . . . . . 8
1110eqeq2d 2446 . . . . . . 7
12 cbvoprab2.3 . . . . . . 7
1311, 12anbi12d 692 . . . . . 6
1413exbidv 1636 . . . . 5
154, 8, 14cbvex 1983 . . . 4
1615exbii 1592 . . 3
1716abbii 2547 . 2
18 df-oprab 6077 . 2
19 df-oprab 6077 . 2
2017, 18, 193eqtr4i 2465 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550  wnf 1553   wceq 1652  cab 2421  cop 3809  coprab 6074 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416 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-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-oprab 6077
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