Theorem bj-nexdvt

Description: Closed form of nexdv . (Contributed by BJ, 20-Oct-2019)

	Ref	Expression
Assertion	bj-nexdvt	⊢ ( ∀ 𝑥 ( 𝜑 → ¬ 𝜓 ) → ( 𝜑 → ¬ ∃ 𝑥 𝜓 ) )

Proof

Step	Hyp	Ref	Expression
1		nfv	⊢ Ⅎ 𝑥 𝜑
2		bj-nexdt	⊢ ( Ⅎ 𝑥 𝜑 → ( ∀ 𝑥 ( 𝜑 → ¬ 𝜓 ) → ( 𝜑 → ¬ ∃ 𝑥 𝜓 ) ) )
3	1 2	ax-mp	⊢ ( ∀ 𝑥 ( 𝜑 → ¬ 𝜓 ) → ( 𝜑 → ¬ ∃ 𝑥 𝜓 ) )