Theorem r19.21bi

Description: Inference from Theorem 19.21 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 20-Nov-1994) (Proof shortened by Wolf Lammen, 11-Jun-2023)

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

Proof

Step	Hyp	Ref	Expression
1		r19.21bi.1	|- ( ph -> A. x e. A ps )
2		rspa	|- ( ( A. x e. A ps /\ x e. A ) -> ps )
3	1 2	sylan	|- ( ( ph /\ x e. A ) -> ps )