Theorem reurex

Description: Restricted unique existence implies restricted existence. (Contributed by NM, 19-Aug-1999)

	Ref	Expression
Assertion	reurex	$$⊢\exists !x\in A\phi \to \exists x\in A\phi$$

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	simplbi	$$⊢\exists !x\in A\phi \to \exists x\in A\phi$$