Theorem vtocl2gf 3169

Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 25-Apr-1995.)

Hypotheses

Ref	Expression
vtocl2gf.1
vtocl2gf.2
vtocl2gf.3
vtocl2gf.4
vtocl2gf.5
vtocl2gf.6
vtocl2gf.7
vtocl2gf.8

Assertion

Ref	Expression
vtocl2gf

Proof of Theorem vtocl2gf

Step	Hyp	Ref	Expression
1		elex 3118	. 2
2		vtocl2gf.3	. . 3
3		vtocl2gf.2	. . . . 5
4	3	nfel1 2635	. . . 4
5		vtocl2gf.5	. . . 4
6	4, 5	nfim 1920	. . 3
7		vtocl2gf.7	. . . 4
8	7	imbi2d 316	. . 3
9		vtocl2gf.1	. . . 4
10		vtocl2gf.4	. . . 4
11		vtocl2gf.6	. . . 4
12		vtocl2gf.8	. . . 4
13	9, 10, 11, 12	vtoclgf 3165	. . 3
14	2, 6, 8, 13	vtoclgf 3165	. 2
15	1, 14	mpan9 469	1

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

This theorem is referenced by:  vtocl3gf  3170  vtocl2g  3171  vtocl2gaf  3174  offval22  6879  fmuldfeqlem1  31576

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-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