Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  vtocl2gf Structured version   Unicode version

Theorem vtocl2gf 3027
 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 2976 . 2
2 vtocl2gf.3 . . 3
3 vtocl2gf.2 . . . . 5
43nfel1 2584 . . . 4
5 vtocl2gf.5 . . . 4
64, 5nfim 1852 . . 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 3023 . . 3
142, 6, 8, 13vtoclgf 3023 . 2
151, 14mpan9 469 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 184   wa 369   wceq 1369  wnf 1589   wcel 1756  wnfc 2561  cvv 2967 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1591  ax-4 1602  ax-5 1670  ax-6 1708  ax-7 1728  ax-10 1775  ax-11 1780  ax-12 1792  ax-13 1943  ax-ext 2419 This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1372  df-ex 1587  df-nf 1590  df-sb 1701  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2969 This theorem is referenced by:  vtocl3gf  3028  vtocl2g  3029  vtocl2gaf  3032  offval22  6647  fmuldfeqlem1  29716
 Copyright terms: Public domain W3C validator