Theorem reurmo

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

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

Proof

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