Theorem nfeu1

Description: Bound-variable hypothesis builder for uniqueness. See also nfeu1ALT . (Contributed by NM, 9-Jul-1994) (Revised by Mario Carneiro, 7-Oct-2016)

	Ref	Expression
Assertion	nfeu1	$$⊢Ⅎx\exists !x\phi$$

Proof

Step	Hyp	Ref	Expression
1		eu6	$$⊢\exists !x\phi \leftrightarrow \exists y\forall x\left(\phi \leftrightarrow x=y\right)$$
2		nfa1	$$⊢Ⅎx\forall x\left(\phi \leftrightarrow x=y\right)$$
3	2	nfex	$$⊢Ⅎx\exists y\forall x\left(\phi \leftrightarrow x=y\right)$$
4	1 3	nfxfr	$$⊢Ⅎx\exists !x\phi$$