Theorem nexdv

Description: Deduction for generalization rule for negated wff. (Contributed by NM, 5-Aug-1993) Reduce dependencies on axioms. (Revised by Wolf Lammen, 13-Jul-2020) (Proof shortened by Wolf Lammen, 10-Oct-2021)

	Ref	Expression
Hypothesis	nexdv.1	$$⊢\phi \to \neg \psi$$
Assertion	nexdv	$$⊢\phi \to \neg \exists x\psi$$

Proof

Step	Hyp	Ref	Expression
1		nexdv.1	$$⊢\phi \to \neg \psi$$
2		ax-5	$$⊢\phi \to \forall x\phi$$
3	2 1	nexdh	$$⊢\phi \to \neg \exists x\psi$$