Theorem equs4v

Description: Version of equs4 with a disjoint variable condition, which requires fewer axioms. (Contributed by NM, 10-May-1993) (Revised by BJ, 31-May-2019)

	Ref	Expression
Assertion	equs4v	$$⊢\forall x\left(x=y\to \phi \right)\to \exists x\left(x=y\wedge \phi \right)$$

Proof

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