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	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
	spei.2	$$⊢\psi$$
Assertion	spei	$$⊢\exists x\phi$$

Proof

Step	Hyp	Ref	Expression
1		spei.1	$$⊢x=y\to \left(\phi \leftrightarrow \psi \right)$$
2		spei.2	$$⊢\psi$$
3		ax6e	$$⊢\exists xx=y$$
4	2 1	mpbiri	$$⊢x=y\to \phi$$
5	3 4	eximii	$$⊢\exists x\phi$$