Theorem exsbim

Description: One direction of the equivalence in exsb is based on fewer axioms. (Contributed by Wolf Lammen, 2-Mar-2023)

	Ref	Expression
Assertion	exsbim	$$⊢\exists y\forall x\left(x=y\to \phi \right)\to \exists x\phi$$

Proof

Step	Hyp	Ref	Expression
1		alequexv	$$⊢\forall x\left(x=y\to \phi \right)\to \exists x\phi$$
2	1	exlimiv	$$⊢\exists y\forall x\left(x=y\to \phi \right)\to \exists x\phi$$