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Theorem cbvoprab2 5855
 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 1509 . . . . . . 7
2 cbvoprab2.1 . . . . . . 7
31, 2nfan 1545 . . . . . 6
43nfex 1617 . . . . 5
5 nfv 1509 . . . . . . 7
6 cbvoprab2.2 . . . . . . 7
75, 6nfan 1545 . . . . . 6
87nfex 1617 . . . . 5
9 opeq2 3715 . . . . . . . . 9
109opeq1d 3720 . . . . . . . 8
1110eqeq2d 2152 . . . . . . 7
12 cbvoprab2.3 . . . . . . 7
1311, 12anbi12d 465 . . . . . 6
1413exbidv 1798 . . . . 5
154, 8, 14cbvex 1730 . . . 4
1615exbii 1585 . . 3
1716abbii 2256 . 2
18 df-oprab 5789 . 2
19 df-oprab 5789 . 2
2017, 18, 193eqtr4i 2171 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1332  wnf 1437  wex 1469  cab 2126  cop 3536  coprab 5786 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 699  ax-5 1424  ax-7 1425  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-10 1484  ax-11 1485  ax-i12 1486  ax-bndl 1487  ax-4 1488  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-i5r 1516  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-3an 965  df-tru 1335  df-nf 1438  df-sb 1737  df-clab 2127  df-cleq 2133  df-clel 2136  df-nfc 2271  df-v 2692  df-un 3081  df-sn 3539  df-pr 3540  df-op 3542  df-oprab 5789 This theorem is referenced by: (None)
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