Theorem ralrimia

Description: Inference from Theorem 19.21 of Margaris p. 90 (restricted quantifier version). (Contributed by Glauco Siliprandi, 23-Oct-2021)

	Ref	Expression
Hypotheses	ralrimia.1	|- F/ x ph
	ralrimia.2	|- ( ( ph /\ x e. A ) -> ps )
Assertion	ralrimia	|- ( ph -> A. x e. A ps )

Proof

Step	Hyp	Ref	Expression
1		ralrimia.1	|- F/ x ph
2		ralrimia.2	|- ( ( ph /\ x e. A ) -> ps )
3	2	ex	|- ( ph -> ( x e. A -> ps ) )
4	1 3	ralrimi	|- ( ph -> A. x e. A ps )