Theorem nfmod

Description: Bound-variable hypothesis builder for the at-most-one quantifier. Deduction version of nfmo . Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfmodv when possible. (Contributed by Mario Carneiro, 14-Nov-2016) (New usage is discouraged.)

	Ref	Expression
Hypotheses	nfmod.1	$$⊢Ⅎy\phi$$
	nfmod.2	$$⊢\phi \to Ⅎx\psi$$
Assertion	nfmod	$$⊢\phi \to Ⅎx{\exists }^{*}y\psi$$

Proof

Step	Hyp	Ref	Expression
1		nfmod.1	$$⊢Ⅎy\phi$$
2		nfmod.2	$$⊢\phi \to Ⅎx\psi$$
3	2	adantr	$$⊢\left(\phi \wedge \neg \forall xx=y\right)\to Ⅎx\psi$$
4	1 3	nfmod2	$$⊢\phi \to Ⅎx{\exists }^{*}y\psi$$