Theorem spei

Description: Inference from existential specialization, using implicit substitution. Remove a distinct variable constraint. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker speiv if possible. (Contributed by NM, 19-Aug-1993) (Proof shortened by Wolf Lammen, 12-May-2018) (New usage is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		spei.1	|- ( x = y -> ( ph <-> ps ) )
2		spei.2	|- ps
3		ax6e	|- E. x x = y
4	2 1	mpbiri	|- ( x = y -> ph )
5	3 4	eximii	|- E. x ph