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Metamath Proof Explorer

Theorem moeuex

Description: Uniqueness implies that existence is equivalent to unique existence. (Contributed by BJ, 7-Oct-2022)

		Ref	Expression
	Assertion	moeuex	$⊢ \exists^{*} x φ \to (\exists x φ \leftrightarrow \exists! x φ)$

Step	Hyp	Ref	Expression
1		df-eu	$⊢ \exists! x φ \leftrightarrow (\exists x φ \land \exists^{*} x φ)$
2	1	rbaibr	$⊢ \exists^{*} x φ \to (\exists x φ \leftrightarrow \exists! x φ)$