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Theorem vtoclgf 3165
 Description: Implicit substitution of a class for a setvar variable, with bound-variable hypotheses in place of disjoint variable restrictions. (Contributed by NM, 21-Sep-2003.) (Proof shortened by Mario Carneiro, 10-Oct-2016.)
Hypotheses
Ref Expression
vtoclgf.1
vtoclgf.2
vtoclgf.3
vtoclgf.4
Assertion
Ref Expression
vtoclgf

Proof of Theorem vtoclgf
StepHypRef Expression
1 elex 3118 . 2
2 vtoclgf.1 . . . 4
32issetf 3114 . . 3
4 vtoclgf.2 . . . 4
5 vtoclgf.4 . . . . 5
6 vtoclgf.3 . . . . 5
75, 6mpbii 211 . . . 4
84, 7exlimi 1912 . . 3
93, 8sylbi 195 . 2
101, 9syl 16 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  E.wex 1612  F/wnf 1616  e.wcel 1818  F/_wnfc 2605   cvv 3109 This theorem is referenced by:  vtocl2gf  3169  vtocl3gf  3170  vtoclgaf  3172  elabgf  3244  ssiun2sf  27427  subtr  30132  subtr2  30133  fsumsplit1  31573  fmuldfeqlem1  31576  fprodsplit1f  31593  climsuse  31614  dvnmptdivc  31735  dvmptfprodlem  31741  stoweidlem59  31841  fourierdlem31  31920 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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