Theorem rexlimiva

Description: Inference from Theorem 19.23 of Margaris p. 90 (restricted quantifier version). (Contributed by NM, 18-Dec-2006) Shorten dependent theorems. (Revised by Wolf lammen, 23-Dec-2024)

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

Proof

Step	Hyp	Ref	Expression
1		rexlimiva.1	|- ( ( x e. A /\ ph ) -> ps )
2		df-rex	|- ( E. x e. A ph <-> E. x ( x e. A /\ ph ) )
3	1	exlimiv	|- ( E. x ( x e. A /\ ph ) -> ps )
4	2 3	sylbi	|- ( E. x e. A ph -> ps )