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Theorem vtocldf 2906
 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 423 . . 3
63, 5alrimi 1765 . 2
7 vtocld.3 . . 3
83, 7alrimi 1765 . 2
9 vtocld.1 . 2
10 vtoclgft 2905 . 2
111, 2, 6, 8, 9, 10syl221anc 1193 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wb 176   wa 358  wal 1540  wnf 1544   wceq 1642   wcel 1710  wnfc 2476 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-an 360  df-3an 936  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:  vtocld  2907
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