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Metamath Proof Explorer

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	$⊢ \neg \forall x \neg φ \to \forall x \neg \forall x \neg φ$

Step	Hyp	Ref	Expression
1		hbn1	$⊢ \neg \forall x \neg φ \to \forall x \neg \forall x \neg φ$