Theorem exmoeub

Description: Existence implies that uniqueness is equivalent to unique existence. (Contributed by NM, 5-Apr-2004)

	Ref	Expression
Assertion	exmoeub	$$⊢\exists x\phi \to \left({\exists }^{*}x\phi \leftrightarrow \exists !x\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		df-eu	$$⊢\exists !x\phi \leftrightarrow \left(\exists x\phi \wedge {\exists }^{*}x\phi \right)$$
2	1	baibr	$$⊢\exists x\phi \to \left({\exists }^{*}x\phi \leftrightarrow \exists !x\phi \right)$$