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Theorem cbvoprab3 6140
 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 1629 . . . . . 6
2 cbvoprab3.1 . . . . . 6
31, 2nfan 1846 . . . . 5
43nfex 1865 . . . 4
54nfex 1865 . . 3
6 nfv 1629 . . . . . 6
7 cbvoprab3.2 . . . . . 6
86, 7nfan 1846 . . . . 5
98nfex 1865 . . . 4
109nfex 1865 . . 3
11 cbvoprab3.3 . . . . 5
1211anbi2d 685 . . . 4
13122exbidv 1638 . . 3
145, 10, 13cbvopab2 4271 . 2
15 dfoprab2 6113 . 2
16 dfoprab2 6113 . 2
1714, 15, 163eqtr4i 2465 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177   wa 359  wex 1550  wnf 1553   wceq 1652  cop 3809  copab 4257  coprab 6074 This theorem is referenced by:  cbvoprab3v  6141  tposoprab  6507  erovlem  6992 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-14 1729  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2416  ax-sep 4322  ax-nul 4330  ax-pr 4395 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-ne 2600  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-opab 4259  df-oprab 6077
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