Theorem nfeuw

Description: Bound-variable hypothesis builder for the unique existential quantifier. Version of nfeu with a disjoint variable condition, which does not require ax-13 . (Contributed by NM, 8-Mar-1995) (Revised by Gino Giotto, 10-Jan-2024)

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

Proof

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