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Theorem vtoclgaf 3172
 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:   ,

Proof of Theorem vtoclgaf
StepHypRef Expression
1 vtoclgaf.1 . . 3
21nfel1 2635 . . . 4
3 vtoclgaf.2 . . . 4
42, 3nfim 1920 . . 3
5 eleq1 2529 . . . 4
6 vtoclgaf.3 . . . 4
75, 6imbi12d 320 . . 3
8 vtoclgaf.4 . . 3
91, 4, 7, 8vtoclgf 3165 . 2
109pm2.43i 47 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  F/wnf 1616  e.wcel 1818  F/_wnfc 2605 This theorem is referenced by:  vtoclga  3173  ssiun2s  4374  fvmptss  5964  fvmptf  5972  fmptco  6064  tfis  6689  inar1  9174  sumss  13546  fprodn0  13783  prmind2  14228  lss1d  17609  itg2splitlem  22155  dgrle  22640  cnlnadjlem5  26990  stoweidlem26  31808 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-an 371  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-v 3111
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