Theorem nfeud

Description: Bound-variable hypothesis builder for the unique existential quantifier. Deduction version of nfeu . Usage of this theorem is discouraged because it depends on ax-13 . Use the weaker nfeudw when possible. (Contributed by NM, 15-Feb-2013) (Revised by Mario Carneiro, 7-Oct-2016) (New usage is discouraged.)

	Ref	Expression
Hypotheses	nfeud.1	$$⊢Ⅎy\phi$$
	nfeud.2	$$⊢\phi \to Ⅎx\psi$$
Assertion	nfeud	$$⊢\phi \to Ⅎx\exists !y\psi$$

Proof

Step	Hyp	Ref	Expression
1		nfeud.1	$$⊢Ⅎy\phi$$
2		nfeud.2	$$⊢\phi \to Ⅎx\psi$$
3	2	adantr	$$⊢\left(\phi \wedge \neg \forall xx=y\right)\to Ⅎx\psi$$
4	1 3	nfeud2	$$⊢\phi \to Ⅎx\exists !y\psi$$