Theorem nfmov

Description: Bound-variable hypothesis builder for the at-most-one quantifier. See nfmo for a version without disjoint variable conditions but requiring ax-13 . (Contributed by NM, 9-Mar-1995) (Revised by Wolf Lammen, 2-Oct-2023)

	Ref	Expression
Hypothesis	nfmov.1	$$⊢Ⅎx\phi$$
Assertion	nfmov	$$⊢Ⅎx{\exists }^{*}y\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfmov.1	$$⊢Ⅎx\phi$$
2		nftru	$$⊢Ⅎy\top$$
3	1	a1i	$$⊢\top \to Ⅎx\phi$$
4	2 3	nfmodv	$$⊢\top \to Ⅎx{\exists }^{*}y\phi$$
5	4	mptru	$$⊢Ⅎx{\exists }^{*}y\phi$$