Theorem rspec 2678

Description: Specialization rule for restricted quantification. (Contributed by NM, 19-Nov-1994.)

Hypothesis

Ref	Expression
rspec.1	|- A.x e. A ph

Assertion

Ref	Expression
rspec	|- (x e. A -> ph)

Proof of Theorem rspec

Step	Hyp	Ref	Expression
1		rspec.1	. 2 |- A.x e. A ph
2		rsp 2674	. 2 |- (A.x e. A ph -> (x e. A -> ph))
3	1, 2	ax-mp 8	1 |- (x e. A -> ph)

Syntax hints:   -> wi 4   e. wcel 1710  A.wral 2614

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-11 1746

This theorem depends on definitions:  df-bi 177  df-ex 1542  df-ral 2619

This theorem is referenced by:  rspec2  2713  vtoclri  2929