Theorem spcgf 3189

Description: Rule of specialization, using implicit substitution. Compare Theorem 7.3 of [Quine] p. 44. (Contributed by NM, 2-Feb-1997.) (Revised by Andrew Salmon, 12-Aug-2011.)

Hypotheses

Ref	Expression
spcgf.1
spcgf.2
spcgf.3

Assertion

Ref	Expression
spcgf

Proof of Theorem spcgf

Step	Hyp	Ref	Expression
1		spcgf.2	. . 3
2		spcgf.1	. . 3
3	1, 2	spcgft 3186	. 2
4		spcgf.3	. 2
5	3, 4	mpg 1620	1

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

This theorem is referenced by:  spcegf  3190  spcgv  3194  rspc  3204  elabgt  3243  eusvnf  4647

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