Theorem nex

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

	Ref	Expression
Hypothesis	nex.1	⊢ ¬ 𝜑
Assertion	nex	⊢ ¬ ∃ 𝑥 𝜑

Proof

Step	Hyp	Ref	Expression
1		nex.1	⊢ ¬ 𝜑
2		alnex	⊢ ( ∀ 𝑥 ¬ 𝜑 ↔ ¬ ∃ 𝑥 𝜑 )
3	2 1	mpgbi	⊢ ¬ ∃ 𝑥 𝜑