Theorem r19.21be

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 21-Nov-1994)

	Ref	Expression
Hypothesis	r19.21be.1	|- ( ph -> A. x e. A ps )
Assertion	r19.21be	|- A. x e. A ( ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		r19.21be.1	|- ( ph -> A. x e. A ps )
2	1	r19.21bi	|- ( ( ph /\ x e. A ) -> ps )
3	2	expcom	|- ( x e. A -> ( ph -> ps ) )
4	3	rgen	|- A. x e. A ( ph -> ps )