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Metamath Proof Explorer

Theorem bj-modalb

Description: A short form of the axiom B of modal logic using only primitive symbols ( -> , -. , A. ). (Contributed by BJ, 4-Apr-2021) (Proof modification is discouraged.)

		Ref	Expression
	Assertion	bj-modalb	$⊢ \neg φ \to \forall x \neg \forall x φ$

Proof

Step	Hyp	Ref	Expression
1		axc7	$⊢ \neg \forall x \neg \forall x φ \to φ$
2	1	con1i	$⊢ \neg φ \to \forall x \neg \forall x φ$