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Theorem vtoclgaf 2618
 Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 17-Feb-2006.) (Revised by Mario Carneiro, 10-Oct-2016.)
Hypotheses
Ref Expression
vtoclgaf.1
vtoclgaf.2
vtoclgaf.3
vtoclgaf.4
Assertion
Ref Expression
vtoclgaf
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem vtoclgaf
StepHypRef Expression
1 vtoclgaf.1 . . 3
21nfel1 2188 . . . 4
3 vtoclgaf.2 . . . 4
42, 3nfim 1464 . . 3
5 eleq1 2100 . . . 4
6 vtoclgaf.3 . . . 4
75, 6imbi12d 223 . . 3
8 vtoclgaf.4 . . 3
91, 4, 7, 8vtoclgf 2612 . 2
109pm2.43i 43 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 98   wceq 1243  wnf 1349   wcel 1393  wnfc 2165 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-v 2559 This theorem is referenced by:  vtoclga  2619  ssiun2s  3701  tfis  4306  fvmptf  5263  fmptco  5330
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