Theorem rgen

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

	Ref	Expression
Hypothesis	rgen.1	|- ( x e. A -> ph )
Assertion	rgen	|- A. x e. A ph

Proof

Step	Hyp	Ref	Expression
1		rgen.1	|- ( x e. A -> ph )
2		df-ral	|- ( A. x e. A ph <-> A. x ( x e. A -> ph ) )
3	2 1	mpgbir	|- A. x e. A ph