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Theorem cbvopab1s 4280
 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 1629 . . . 4
2 nfv 1629 . . . . . 6
3 nfs1v 2182 . . . . . 6
42, 3nfan 1846 . . . . 5
54nfex 1865 . . . 4
6 opeq1 3984 . . . . . . 7
76eqeq2d 2447 . . . . . 6
8 sbequ12 1944 . . . . . 6
97, 8anbi12d 692 . . . . 5
109exbidv 1636 . . . 4
111, 5, 10cbvex 1983 . . 3
1211abbii 2548 . 2
13 df-opab 4267 . 2
14 df-opab 4267 . 2
1512, 13, 143eqtr4i 2466 1
 Colors of variables: wff set class Syntax hints:   wa 359  wex 1550   wceq 1652  wsb 1658  cab 2422  cop 3817  copab 4265 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-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417 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 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-rab 2714  df-v 2958  df-dif 3323  df-un 3325  df-in 3327  df-ss 3334  df-nul 3629  df-if 3740  df-sn 3820  df-pr 3821  df-op 3823  df-opab 4267
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