Theorem bj-hbnaeb

Description: Biconditional version of hbnae (to replace it?). (Contributed by BJ, 6-Oct-2018)

	Ref	Expression
Assertion	bj-hbnaeb	$$⊢\neg \forall xx=y\leftrightarrow \forall z\neg \forall xx=y$$

Proof

Step	Hyp	Ref	Expression
1		hbnae	$$⊢\neg \forall xx=y\to \forall z\neg \forall xx=y$$
2		sp	$$⊢\forall z\neg \forall xx=y\to \neg \forall xx=y$$
3	1 2	impbii	$$⊢\neg \forall xx=y\leftrightarrow \forall z\neg \forall xx=y$$