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Theorem vtocldf 2651
 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 113 . . 3
63, 5alrimi 1456 . 2
7 vtocld.3 . . 3
83, 7alrimi 1456 . 2
9 vtocld.1 . 2
10 vtoclgft 2650 . 2
111, 2, 6, 8, 9, 10syl221anc 1181 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 102   wb 103  wal 1283   wceq 1285  wnf 1390   wcel 1434  wnfc 2207 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2064 This theorem depends on definitions:  df-bi 115  df-3an 922  df-nf 1391  df-sb 1687  df-clab 2069  df-cleq 2075  df-clel 2078  df-nfc 2209  df-v 2604 This theorem is referenced by:  vtocld  2652  peano2  4344  iota2df  4921
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