Theorem nex

Description: Generalization rule for negated wff. (Contributed by NM, 18-May-1994)

	Ref	Expression
Hypothesis	nex.1	$$⊢\neg \phi$$
Assertion	nex	$$⊢\neg \exists x\phi$$

Proof

Step	Hyp	Ref	Expression
1		nex.1	$$⊢\neg \phi$$
2		alnex	$$⊢\forall x\neg \phi \leftrightarrow \neg \exists x\phi$$
3	2 1	mpgbi	$$⊢\neg \exists x\phi$$