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Theorem vtocl2gf 3119
 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 3068 . 2
2 vtocl2gf.3 . . 3
3 vtocl2gf.2 . . . . 5
43nfel1 2580 . . . 4
5 vtocl2gf.5 . . . 4
64, 5nfim 1948 . . 3
7 vtocl2gf.7 . . . 4
87imbi2d 314 . . 3
9 vtocl2gf.1 . . . 4
10 vtocl2gf.4 . . . 4
11 vtocl2gf.6 . . . 4
12 vtocl2gf.8 . . . 4
139, 10, 11, 12vtoclgf 3115 . . 3
142, 6, 8, 13vtoclgf 3115 . 2
151, 14mpan9 467 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 367   wceq 1405  wnf 1637   wcel 1842  wnfc 2550  cvv 3059 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380 This theorem depends on definitions:  df-bi 185  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-v 3061 This theorem is referenced by:  vtocl3gf  3120  vtocl2g  3121  vtocl2gaf  3124  offval22  6863  fmuldfeqlem1  36944
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