Theorem vtocl3gf 3170

Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 10-Aug-2013.) (Revised by Mario Carneiro, 10-Oct-2016.)

Hypotheses

Ref	Expression
vtocl3gf.a
vtocl3gf.b
vtocl3gf.c
vtocl3gf.d
vtocl3gf.e
vtocl3gf.f
vtocl3gf.1
vtocl3gf.2
vtocl3gf.3
vtocl3gf.4
vtocl3gf.5
vtocl3gf.6
vtocl3gf.7

Assertion

Ref	Expression
vtocl3gf

Proof of Theorem vtocl3gf

Step	Hyp	Ref	Expression
1		elex 3118	. . 3
2		vtocl3gf.d	. . . 4
3		vtocl3gf.e	. . . 4
4		vtocl3gf.f	. . . 4
5		vtocl3gf.b	. . . . . 6
6	5	nfel1 2635	. . . . 5
7		vtocl3gf.2	. . . . 5
8	6, 7	nfim 1920	. . . 4
9		vtocl3gf.c	. . . . . 6
10	9	nfel1 2635	. . . . 5
11		vtocl3gf.3	. . . . 5
12	10, 11	nfim 1920	. . . 4
13		vtocl3gf.5	. . . . 5
14	13	imbi2d 316	. . . 4
15		vtocl3gf.6	. . . . 5
16	15	imbi2d 316	. . . 4
17		vtocl3gf.a	. . . . 5
18		vtocl3gf.1	. . . . 5
19		vtocl3gf.4	. . . . 5
20		vtocl3gf.7	. . . . 5
21	17, 18, 19, 20	vtoclgf 3165	. . . 4
22	2, 3, 4, 8, 12, 14, 16, 21	vtocl2gf 3169	. . 3
23	1, 22	mpan9 469	. 2
24	23	3impb 1192	1

Syntax hints:  ->wi 4  <->wb 184  /\wa 369  /\w3a 973  =wceq 1395  F/wnf 1616  e.wcel 1818  F/_wnfc 2605  cvv 3109

This theorem is referenced by:  vtocl3gaf  3176

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