Theorem nfeu

Description: Bound-variable hypothesis builder for the unique existential quantifier. Note that x and y need not be disjoint. Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfeuw when possible. (Contributed by NM, 8-Mar-1995) (Revised by Mario Carneiro, 7-Oct-2016) (New usage is discouraged.)

	Ref	Expression
Hypothesis	nfeu.1	$$⊢Ⅎx\phi$$
Assertion	nfeu	$$⊢Ⅎx\exists !y\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfeu.1	$$⊢Ⅎx\phi$$
2		nftru	$$⊢Ⅎy\top$$
3	1	a1i	$$⊢\top \to Ⅎx\phi$$
4	2 3	nfeud	$$⊢\top \to Ⅎx\exists !y\phi$$
5	4	mptru	$$⊢Ⅎx\exists !y\phi$$