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Theorem vtocldf 3158
 Description: Implicit substitution of a class for a setvar variable. (Contributed by Mario Carneiro, 15-Oct-2016.)
Hypotheses
Ref Expression
vtocld.1
vtocld.2
vtocld.3
vtocldf.4
vtocldf.5
vtocldf.6
Assertion
Ref Expression
vtocldf

Proof of Theorem vtocldf
StepHypRef Expression
1 vtocldf.5 . 2
2 vtocldf.6 . 2
3 vtocldf.4 . . 3
4 vtocld.2 . . . 4
54ex 434 . . 3
63, 5alrimi 1877 . 2
7 vtocld.3 . . 3
83, 7alrimi 1877 . 2
9 vtocld.1 . 2
10 vtoclgft 3157 . 2
111, 2, 6, 8, 9, 10syl221anc 1239 1
 Colors of variables: wff setvar class Syntax hints:  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  F/wnf 1616  e.wcel 1818  F/_wnfc 2605 This theorem is referenced by:  vtocld  3159  iota2df  5580  riotasv2d  34688 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435 This theorem depends on definitions:  df-bi 185  df-an 371  df-3an 975  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-v 3111
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