Theorem ax5e

Description: A rephrasing of ax-5 using the existential quantifier. (Contributed by Wolf Lammen, 4-Dec-2017)

	Ref	Expression
Assertion	ax5e	$$⊢\exists x\phi \to \phi$$

Proof

Step	Hyp	Ref	Expression
1		ax-5	$$⊢\neg \phi \to \forall x\neg \phi$$
2		eximal	$$⊢\left(\exists x\phi \to \phi \right)\leftrightarrow \left(\neg \phi \to \forall x\neg \phi \right)$$
3	1 2	mpbir	$$⊢\exists x\phi \to \phi$$