Theorem rspec 1694

Description: Specialization rule for restricted quantification.

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		ra4 1691	. 2 |- (A.x e. A ph -> (x e. A -> ph))
3	1, 2	ax-mp 7	1 |- (x e. A -> ph)

Syntax hints:   -> wi 3   e. wcel 956  A.wral 1642

This theorem is referenced by:  rspec2 1723  vtoclri 1855  isarep2 3570  indstr 6401  cvgcmp3cetlem1 7132  cvgcmp3cetlem2 7133

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7  ax-4 971

This theorem depends on definitions:  df-bi 147  df-ral 1646

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