Theorem axc7e

Description: Abbreviated version of axc7 using the existential quantifier. Corresponds to the dual of Axiom (B) of modal logic. (Contributed by NM, 5-Aug-1993) (Proof shortened by Wolf Lammen, 8-Jul-2022)

	Ref	Expression
Assertion	axc7e	$$⊢\exists x\forall x\phi \to \phi$$

Proof

Step	Hyp	Ref	Expression
1		hbe1a	$$⊢\exists x\forall x\phi \to \forall x\phi$$
2	1	19.21bi	$$⊢\exists x\forall x\phi \to \phi$$