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

Step	Hyp	Ref	Expression
1		vtocldf.5	. 2
2		vtocldf.6	. 2
3		vtocldf.4	. . 3
4		vtocld.2	. . . 4
5	4	ex 434	. . 3
6	3, 5	alrimi 1877	. 2
7		vtocld.3	. . 3
8	3, 7	alrimi 1877	. 2
9		vtocld.1	. 2
10		vtoclgft 3157	. 2
11	1, 2, 6, 8, 9, 10	syl221anc 1239	1

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