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Metamath Proof Explorer

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	$⊢ \exists x (x = y \land φ)$
	Assertion	sbalexi	$⊢ \forall x (x = y \to φ)$

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