Theorem rspec 2458

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 2454	. 2 |- ( A. x e. A ph -> ( x e. A -> ph ) )
3	1, 2	ax-mp 7	1 |- ( x e. A -> ph )

Syntax hints:   -> wi 4   e. wcel 1463   A.wral 2390

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-4 1470

This theorem depends on definitions:  df-bi 116  df-ral 2395

This theorem is referenced by:  rspec2  2495  vtoclri  2732  isarep2  5168  ecopover  6481  ecopoverg  6484  indstr  9290