Theorem modal5

Description: The analogue in our predicate calculus of axiom (5) of modal logic S5. See also hbe1 . (Contributed by NM, 5-Oct-2005)

	Ref	Expression
Assertion	modal5	⊢ ( ¬ ∀ 𝑥 ¬ 𝜑 → ∀ 𝑥 ¬ ∀ 𝑥 ¬ 𝜑 )

Proof

Step	Hyp	Ref	Expression
1		hbn1	⊢ ( ¬ ∀ 𝑥 ¬ 𝜑 → ∀ 𝑥 ¬ ∀ 𝑥 ¬ 𝜑 )