Theorem spcegf 3190

Description: Existential specialization, using implicit substitution. (Contributed by NM, 2-Feb-1997.)

Hypotheses

Ref	Expression
spcgf.1
spcgf.2
spcgf.3

Assertion

Ref	Expression
spcegf

Proof of Theorem spcegf

Step	Hyp	Ref	Expression
1		spcgf.1	. . . 4
2		spcgf.2	. . . . 5
3	2	nfn 1901	. . . 4
4		spcgf.3	. . . . 5
5	4	notbid 294	. . . 4
6	1, 3, 5	spcgf 3189	. . 3
7	6	con2d 115	. 2
8		df-ex 1613	. 2
9	7, 8	syl6ibr 227	1

Syntax hints:  -.wn 3  ->wi 4  <->wb 184  A.wal 1393  =wceq 1395  E.wex 1612  F/wnf 1616  e.wcel 1818  F/_wnfc 2605

This theorem is referenced by:  spcegv  3195  rspce  3205  euotd  4753  rspcegf  31398  stoweidlem36  31818  stoweidlem46  31828  bnj607  33974  bnj1491  34113

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