Theorem spcimdv 3191

Description: Restricted specialization, using implicit substitution. (Contributed by Mario Carneiro, 4-Jan-2017.)

Hypotheses

Ref	Expression
spcimdv.1
spcimdv.2

Assertion

Ref	Expression
spcimdv

Distinct variable groups:   ,   ,   ,

Proof of Theorem spcimdv

Step	Hyp	Ref	Expression
1		spcimdv.2	. . . 4
2	1	ex 434	. . 3
3	2	alrimiv 1719	. 2
4		spcimdv.1	. 2
5		nfv 1707	. . 3
6		nfcv 2619	. . 3
7	5, 6	spcimgft 3185	. 2
8	3, 4, 7	sylc 60	1

Syntax hints:  ->wi 4  /\wa 369  A.wal 1393  =wceq 1395  e.wcel 1818

This theorem is referenced by:  spcdv  3192  spcimedv  3193  rspcimdv  3211  mrieqv2d  15036  mreexexlemd  15041

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