Theorem nfmo

Description: Bound-variable hypothesis builder for the at-most-one 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 nfmov when possible. (Contributed by NM, 9-Mar-1995) (New usage is discouraged.)

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

Proof

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