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Theorem vtocl2gf 2743
 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 2692 . 2
2 vtocl2gf.3 . . 3
3 vtocl2gf.2 . . . . 5
43nfel1 2290 . . . 4
5 vtocl2gf.5 . . . 4
64, 5nfim 1551 . . 3
7 vtocl2gf.7 . . . 4
87imbi2d 229 . . 3
9 vtocl2gf.1 . . . 4
10 vtocl2gf.4 . . . 4
11 vtocl2gf.6 . . . 4
12 vtocl2gf.8 . . . 4
139, 10, 11, 12vtoclgf 2739 . . 3
142, 6, 8, 13vtoclgf 2739 . 2
151, 14mpan9 279 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104   wceq 1331  wnf 1436   wcel 1480  wnfc 2266  cvv 2681 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2119 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2124  df-cleq 2130  df-clel 2133  df-nfc 2268  df-v 2683 This theorem is referenced by:  vtocl3gf  2744  vtocl2g  2745  vtocl2gaf  2748
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