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Theorem vtoclf 2908
 Description: Implicit substitution of a class for a setvar variable. This is a generalization of chvar 1986. (Contributed by NM, 30-Aug-1993.)
Hypotheses
Ref Expression
vtoclf.1
vtoclf.2
vtoclf.3
vtoclf.4
Assertion
Ref Expression
vtoclf
Distinct variable group:   ,
Allowed substitution hints:   ()   ()

Proof of Theorem vtoclf
StepHypRef Expression
1 vtoclf.1 . . 3
2 vtoclf.2 . . . . 5
32isseti 2865 . . . 4
4 vtoclf.3 . . . . . 6
54biimpd 198 . . . . 5
65eximi 1576 . . . 4
73, 6ax-mp 8 . . 3
81, 719.36i 1872 . 2
9 vtoclf.4 . 2
108, 9mpg 1548 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176  wex 1541  wnf 1544   wceq 1642   wcel 1710  cvv 2859 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-v 2861 This theorem is referenced by:  vtocl  2909
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