Theorem euabex

Description: The abstraction of a wff with existential uniqueness exists. (Contributed by NM, 25-Nov-1994)

	Ref	Expression
Assertion	euabex	$$⊢\exists !x\phi \to \left\{x|\phi \right\}\in \mathrm{V}$$

Proof

Step	Hyp	Ref	Expression
1		eumo	$$⊢\exists !x\phi \to {\exists }^{*}x\phi$$
2		moabex	$$⊢{\exists }^{*}x\phi \to \left\{x|\phi \right\}\in \mathrm{V}$$
3	1 2	syl	$$⊢\exists !x\phi \to \left\{x|\phi \right\}\in \mathrm{V}$$