Theorem exlimih

Description: Inference associated with 19.23 . See exlimiv for a version with a disjoint variable condition requiring fewer axioms. (Contributed by NM, 10-Jan-1993) (Proof shortened by Andrew Salmon, 13-May-2011) (Proof shortened by Wolf Lammen, 1-Jan-2018)

	Ref	Expression
Hypotheses	exlimih.1	|- ( ps -> A. x ps )
	exlimih.2	|- ( ph -> ps )
Assertion	exlimih	|- ( E. x ph -> ps )

Proof

Step	Hyp	Ref	Expression
1		exlimih.1	|- ( ps -> A. x ps )
2		exlimih.2	|- ( ph -> ps )
3	1	nf5i	|- F/ x ps
4	3 2	exlimi	|- ( E. x ph -> ps )