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Theorem vtoclgf 2913
 Description: Implicit substitution of a class for a setvar variable, with bound-variable hypotheses in place of distinct variable restrictions. (Contributed by NM, 21-Sep-2003.) (Proof shortened by Mario Carneiro, 10-Oct-2016.)
Hypotheses
Ref Expression
vtoclgf.1
vtoclgf.2
vtoclgf.3
vtoclgf.4
Assertion
Ref Expression
vtoclgf

Proof of Theorem vtoclgf
StepHypRef Expression
1 elex 2867 . 2
2 vtoclgf.1 . . . 4
32issetf 2864 . . 3
4 vtoclgf.2 . . . 4
5 vtoclgf.4 . . . . 5
6 vtoclgf.3 . . . . 5
75, 6mpbii 202 . . . 4
84, 7exlimi 1803 . . 3
93, 8sylbi 187 . 2
101, 9syl 15 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176  wex 1541  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:  vtoclg  2914  vtocl2gf  2916  vtocl3gf  2917  vtoclgaf  2919  ceqsexg  2970  elabgf  2983  mob  3018  opeliunxp2  4822
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