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Metamath Proof Explorer

Theorem eumo

Description: Existential uniqueness implies uniqueness. (Contributed by NM, 23-Mar-1995)

		Ref	Expression
	Assertion	eumo	$⊢ \exists! x φ \to \exists^{*} x φ$

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