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Metamath Proof Explorer

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

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