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Theorem vtoclgf 2770
 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 2723 . 2
2 vtoclgf.1 . . . 4
32issetf 2719 . . 3
4 vtoclgf.2 . . . 4
5 vtoclgf.4 . . . . 5
6 vtoclgf.3 . . . . 5
75, 6mpbii 147 . . . 4
84, 7exlimi 1574 . . 3
93, 8sylbi 120 . 2
101, 9syl 14 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1335  wnf 1440  wex 1472   wcel 2128  wnfc 2286  cvv 2712 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 699  ax-5 1427  ax-7 1428  ax-gen 1429  ax-ie1 1473  ax-ie2 1474  ax-8 1484  ax-10 1485  ax-11 1486  ax-i12 1487  ax-bndl 1489  ax-4 1490  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2139 This theorem depends on definitions:  df-bi 116  df-tru 1338  df-nf 1441  df-sb 1743  df-clab 2144  df-cleq 2150  df-clel 2153  df-nfc 2288  df-v 2714 This theorem is referenced by:  vtoclg  2772  vtocl2gf  2774  vtocl3gf  2775  vtoclgaf  2777  ceqsexg  2840  elabgf  2854  mob  2894  opeliunxp2  4723  fvmptss2  5540
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