Theorem alequexv

Description: Version of equs4v with its consequence simplified by exsimpr . (Contributed by BJ, 9-Nov-2021)

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

Proof

Step	Hyp	Ref	Expression
1		ax6ev	$$⊢\exists xx=y$$
2		exim	$$⊢\forall x\left(x=y\to \phi \right)\to \left(\exists xx=y\to \exists x\phi \right)$$
3	1 2	mpi	$$⊢\forall x\left(x=y\to \phi \right)\to \exists x\phi$$