Theorem vtoclgaf 3172

Description: Implicit substitution of a class for a setvar variable. (Contributed by NM, 17-Feb-2006.) (Revised by Mario Carneiro, 10-Oct-2016.)

Hypotheses

Ref	Expression
vtoclgaf.1
vtoclgaf.2
vtoclgaf.3
vtoclgaf.4

Assertion

Ref	Expression
vtoclgaf

Distinct variable group:   ,

Proof of Theorem vtoclgaf

Step	Hyp	Ref	Expression
1		vtoclgaf.1	. . 3
2	1	nfel1 2635	. . . 4
3		vtoclgaf.2	. . . 4
4	2, 3	nfim 1920	. . 3
5		eleq1 2529	. . . 4
6		vtoclgaf.3	. . . 4
7	5, 6	imbi12d 320	. . 3
8		vtoclgaf.4	. . 3
9	1, 4, 7, 8	vtoclgf 3165	. 2
10	9	pm2.43i 47	1

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

This theorem is referenced by:  vtoclga  3173  ssiun2s  4374  fvmptss  5964  fvmptf  5972  fmptco  6064  tfis  6689  inar1  9174  sumss  13546  fprodn0  13783  prmind2  14228  lss1d  17609  itg2splitlem  22155  dgrle  22640  cnlnadjlem5  26990  stoweidlem26  31808

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