Theorem ralrimi

Description: Inference from Theorem 19.21 of Margaris p. 90 (restricted quantifier version). (Contributed by NM, 10-Oct-1999) Shortened after introduction of hbralrimi . (Revised by Wolf Lammen, 4-Dec-2019)

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

Proof

Step	Hyp	Ref	Expression
1		ralrimi.1	|- F/ x ph
2		ralrimi.2	|- ( ph -> ( x e. A -> ps ) )
3	1	nf5ri	|- ( ph -> A. x ph )
4	3 2	hbralrimi	|- ( ph -> A. x e. A ps )