Theorem eumo

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

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

Proof

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