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Theorem vtocl2gf 3169
 Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 25-Apr-1995.)
Hypotheses
Ref Expression
vtocl2gf.1
vtocl2gf.2
vtocl2gf.3
vtocl2gf.4
vtocl2gf.5
vtocl2gf.6
vtocl2gf.7
vtocl2gf.8
Assertion
Ref Expression
vtocl2gf

Proof of Theorem vtocl2gf
StepHypRef Expression
1 elex 3118 . 2
2 vtocl2gf.3 . . 3
3 vtocl2gf.2 . . . . 5
43nfel1 2635 . . . 4
5 vtocl2gf.5 . . . 4
64, 5nfim 1920 . . 3
7 vtocl2gf.7 . . . 4
87imbi2d 316 . . 3
9 vtocl2gf.1 . . . 4
10 vtocl2gf.4 . . . 4
11 vtocl2gf.6 . . . 4
12 vtocl2gf.8 . . . 4
139, 10, 11, 12vtoclgf 3165 . . 3
142, 6, 8, 13vtoclgf 3165 . 2
151, 14mpan9 469 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  F/wnf 1616  e.wcel 1818  F/_wnfc 2605   cvv 3109 This theorem is referenced by:  vtocl3gf  3170  vtocl2g  3171  vtocl2gaf  3174  offval22  6879  fmuldfeqlem1  31576 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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