Theorem spimehOLD

Description: Obsolete version of spimew as of 22-Oct-2023. (Contributed by NM, 7-Aug-1994) (Proof shortened by Wolf Lammen, 10-Dec-2017) (New usage is discouraged.) (Proof modification is discouraged.)

	Ref	Expression
Hypotheses	spimew.1	$$⊢\phi \to \forall x\phi$$
	spimew.2	$$⊢x=y\to \left(\phi \to \psi \right)$$
Assertion	spimehOLD	$$⊢\phi \to \exists x\psi$$

Proof

Step	Hyp	Ref	Expression
1		spimew.1	$$⊢\phi \to \forall x\phi$$
2		spimew.2	$$⊢x=y\to \left(\phi \to \psi \right)$$
3		ax6ev	$$⊢\exists xx=y$$
4	3 2	eximii	$$⊢\exists x\left(\phi \to \psi \right)$$
5	4	19.35i	$$⊢\forall x\phi \to \exists x\psi$$
6	1 5	syl	$$⊢\phi \to \exists x\psi$$