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Theorem cbvoprab3 5840
 Description: Rule used to change the third bound variable in an operation abstraction, using implicit substitution. (Contributed by NM, 22-Aug-2013.)
Hypotheses
Ref Expression
cbvoprab3.1
cbvoprab3.2
cbvoprab3.3
Assertion
Ref Expression
cbvoprab3
Distinct variable groups:   ,,   ,,
Allowed substitution hints:   (,,,)   (,,,)

Proof of Theorem cbvoprab3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1508 . . . . . 6
2 cbvoprab3.1 . . . . . 6
31, 2nfan 1544 . . . . 5
43nfex 1616 . . . 4
54nfex 1616 . . 3
6 nfv 1508 . . . . . 6
7 cbvoprab3.2 . . . . . 6
86, 7nfan 1544 . . . . 5
98nfex 1616 . . . 4
109nfex 1616 . . 3
11 cbvoprab3.3 . . . . 5
1211anbi2d 459 . . . 4
13122exbidv 1840 . . 3
145, 10, 13cbvopab2 3997 . 2
15 dfoprab2 5811 . 2
16 dfoprab2 5811 . 2
1714, 15, 163eqtr4i 2168 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1331  wnf 1436  wex 1468  cop 3525  copab 3983  coprab 5768 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 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-14 1492  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119  ax-sep 4041  ax-pow 4093  ax-pr 4126 This theorem depends on definitions:  df-bi 116  df-3an 964  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683  df-un 3070  df-in 3072  df-ss 3079  df-pw 3507  df-sn 3528  df-pr 3529  df-op 3531  df-opab 3985  df-oprab 5771 This theorem is referenced by:  cbvoprab3v  5841  tposoprab  6170  erovlem  6514
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