Theorem rspec 2518

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 2513	. 2 |- ( A. x e. A ph -> ( x e. A -> ph ) )
3	1, 2	ax-mp 5	1 |- ( x e. A -> ph )

Syntax hints:   -> wi 4   e. wcel 2136   A.wral 2444

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1498

This theorem depends on definitions:  df-bi 116  df-ral 2449

This theorem is referenced by:  rspec2  2555  vtoclri  2801  isarep2  5275  mpoexw  6181  ecopover  6599  ecopoverg  6602  indstr  9531