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	$$⊢\neg \phi \to \forall x\neg \forall x\phi$$

Proof

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