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Theorem cbvopab1s 4475
 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:   ,,   ,
Allowed substitution hints:   (,)

Proof of Theorem cbvopab1s
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 nfv 1761 . . . 4
2 nfv 1761 . . . . . 6
3 nfs1v 2266 . . . . . 6
42, 3nfan 2011 . . . . 5
54nfex 2031 . . . 4
6 opeq1 4166 . . . . . . 7
76eqeq2d 2461 . . . . . 6
8 sbequ12 2083 . . . . . 6
97, 8anbi12d 717 . . . . 5
109exbidv 1768 . . . 4
111, 5, 10cbvex 2115 . . 3
1211abbii 2567 . 2
13 df-opab 4462 . 2
14 df-opab 4462 . 2
1512, 13, 143eqtr4i 2483 1
 Colors of variables: wff setvar class Syntax hints:   wa 371   wceq 1444  wex 1663  wsb 1797  cab 2437  cop 3974  copab 4460 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1669  ax-4 1682  ax-5 1758  ax-6 1805  ax-7 1851  ax-10 1915  ax-11 1920  ax-12 1933  ax-13 2091  ax-ext 2431 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-3an 987  df-tru 1447  df-ex 1664  df-nf 1668  df-sb 1798  df-clab 2438  df-cleq 2444  df-clel 2447  df-nfc 2581  df-rab 2746  df-v 3047  df-dif 3407  df-un 3409  df-in 3411  df-ss 3418  df-nul 3732  df-if 3882  df-sn 3969  df-pr 3971  df-op 3975  df-opab 4462 This theorem is referenced by: (None)
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