Theorem vtoclgf 3165

Description: Implicit substitution of a class for a setvar variable, with bound-variable hypotheses in place of disjoint variable restrictions. (Contributed by NM, 21-Sep-2003.) (Proof shortened by Mario Carneiro, 10-Oct-2016.)

Hypotheses

Ref	Expression
vtoclgf.1
vtoclgf.2
vtoclgf.3
vtoclgf.4

Assertion

Ref	Expression
vtoclgf

Proof of Theorem vtoclgf

Step	Hyp	Ref	Expression
1		elex 3118	. 2
2		vtoclgf.1	. . . 4
3	2	issetf 3114	. . 3
4		vtoclgf.2	. . . 4
5		vtoclgf.4	. . . . 5
6		vtoclgf.3	. . . . 5
7	5, 6	mpbii 211	. . . 4
8	4, 7	exlimi 1912	. . 3
9	3, 8	sylbi 195	. 2
10	1, 9	syl 16	1

Syntax hints:  ->wi 4  <->wb 184  =wceq 1395  E.wex 1612  F/wnf 1616  e.wcel 1818  F/_wnfc 2605  cvv 3109

This theorem is referenced by:  vtocl2gf  3169  vtocl3gf  3170  vtoclgaf  3172  elabgf  3244  ssiun2sf  27427  subtr  30132  subtr2  30133  fsumsplit1  31573  fmuldfeqlem1  31576  fprodsplit1f  31593  climsuse  31614  dvnmptdivc  31735  dvmptfprodlem  31741  stoweidlem59  31841  fourierdlem31  31920

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