New Foundations Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  NFE Home  >  Th. List  >  vtocl2gf Unicode version

Theorem vtocl2gf 2916
 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 2867 . 2
2 vtocl2gf.3 . . 3
3 vtocl2gf.2 . . . . 5
43nfel1 2499 . . . 4
5 vtocl2gf.5 . . . 4
64, 5nfim 1813 . . 3
7 vtocl2gf.7 . . . 4
87imbi2d 307 . . 3
9 vtocl2gf.1 . . . 4
10 vtocl2gf.4 . . . 4
11 vtocl2gf.6 . . . 4
12 vtocl2gf.8 . . . 4
139, 10, 11, 12vtoclgf 2913 . . 3
142, 6, 8, 13vtoclgf 2913 . 2
151, 14mpan9 455 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wnf 1544   wceq 1642   wcel 1710  wnfc 2476  cvv 2859 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861 This theorem is referenced by:  vtocl3gf  2917  vtocl2g  2918  vtocl2gaf  2921
 Copyright terms: Public domain W3C validator