Theorem nexd

Description: Deduction for generalization rule for negated wff. (Contributed by Mario Carneiro, 24-Sep-2016)

	Ref	Expression
Hypotheses	nexd.1	$$⊢Ⅎx\phi$$
	nexd.2	$$⊢\phi \to \neg \psi$$
Assertion	nexd	$$⊢\phi \to \neg \exists x\psi$$

Proof

Step	Hyp	Ref	Expression
1		nexd.1	$$⊢Ⅎx\phi$$
2		nexd.2	$$⊢\phi \to \neg \psi$$
3	1	nf5ri	$$⊢\phi \to \forall x\phi$$
4	3 2	nexdh	$$⊢\phi \to \neg \exists x\psi$$