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Theorem cbvopab1s 4524
Description: Change first bound variable in an ordered-pair class abstraction, using explicit substitution. (Contributed by NM, 31-Jul-2003.)
Assertion
Ref Expression
cbvopab1s
Distinct variable groups:   , ,   ,

Proof of Theorem cbvopab1s
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1707 . . . 4
2 nfv 1707 . . . . . 6
3 nfs1v 2181 . . . . . 6
42, 3nfan 1928 . . . . 5
54nfex 1948 . . . 4
6 opeq1 4217 . . . . . . 7
76eqeq2d 2471 . . . . . 6
8 sbequ12 1992 . . . . . 6
97, 8anbi12d 710 . . . . 5
109exbidv 1714 . . . 4
111, 5, 10cbvex 2022 . . 3
1211abbii 2591 . 2
13 df-opab 4511 . 2
14 df-opab 4511 . 2
1512, 13, 143eqtr4i 2496 1
Colors of variables: wff setvar class
Syntax hints:  /\wa 369  =wceq 1395  E.wex 1612  [wsb 1739  {cab 2442  <.cop 4035  {copab 4509
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-rab 2816  df-v 3111  df-dif 3478  df-un 3480  df-in 3482  df-ss 3489  df-nul 3785  df-if 3942  df-sn 4030  df-pr 4032  df-op 4036  df-opab 4511
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