Theorem speiv

Description: Inference from existential specialization. (Contributed by NM, 19-Aug-1993) (Revised by Wolf Lammen, 22-Oct-2023)

	Ref	Expression
Hypotheses	speiv.1	|- ( x = y -> ( ps -> ph ) )
	speiv.2	|- ps
Assertion	speiv	|- E. x ph

Proof

Step	Hyp	Ref	Expression
1		speiv.1	|- ( x = y -> ( ps -> ph ) )
2		speiv.2	|- ps
3	2	hbth	|- ( ps -> A. x ps )
4	3 1	spimew	|- ( ps -> E. x ph )
5	2 4	ax-mp	|- E. x ph