Theorem sbalexi

Description: Inference form of sbalex , avoiding ax-10 by using ax-gen . (Contributed by SN, 12-Aug-2025)

	Ref	Expression
Hypothesis	sbalexi.1	$$⊢\exists x\left(x=y\wedge \phi \right)$$
Assertion	sbalexi	$$⊢\forall x\left(x=y\to \phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		sbalexi.1	$$⊢\exists x\left(x=y\wedge \phi \right)$$
2		ax12ev2	$$⊢\exists x\left(x=y\wedge \phi \right)\to \left(x=y\to \phi \right)$$
3	1 2	ax-mp	$$⊢x=y\to \phi$$
4	3	ax-gen	$$⊢\forall x\left(x=y\to \phi \right)$$