Theorem rspec 2584

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 2579	. 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 2202   A.wral 2510

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1558

This theorem depends on definitions:  df-bi 117  df-ral 2515

This theorem is referenced by:  rspec2  2621  vtoclri  2881  isarep2  5417  mpoexw  6377  ecopover  6801  ecopoverg  6804  indstr  9826