Theorem rexlimiv

Description: Inference from Theorem 19.23 of Margaris p. 90. (Restricted quantifier version.) (Contributed by NM, 20-Nov-1994) Reduce dependencies on axioms. (Revised by Wolf Lammen, 14-Jan-2020)

	Ref	Expression
Hypothesis	rexlimiv.1	|- ( x e. A -> ( ph -> ps ) )
Assertion	rexlimiv	|- ( E. x e. A ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		rexlimiv.1	|- ( x e. A -> ( ph -> ps ) )
2	1	rgen	|- A. x e. A ( ph -> ps )
3		r19.23v	|- ( A. x e. A ( ph -> ps ) <-> ( E. x e. A ph -> ps ) )
4	2 3	mpbi	|- ( E. x e. A ph -> ps )