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Metamath Proof Explorer

Theorem reurmo

Description: Restricted existential uniqueness implies restricted "at most one." (Contributed by NM, 16-Jun-2017)

		Ref	Expression
	Assertion	reurmo	$⊢ \exists! x \in A φ \to \exists^{*} x \in A φ$

Step	Hyp	Ref	Expression
1		reu5	$⊢ \exists! x \in A φ \leftrightarrow (\exists x \in A φ \land \exists^{*} x \in A φ)$
2	1	simprbi	$⊢ \exists! x \in A φ \to \exists^{*} x \in A φ$