Theorem bj-hbaeb

Description: Biconditional version of hbae . (Contributed by BJ, 6-Oct-2018) (Proof modification is discouraged.)

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

Proof

Step	Hyp	Ref	Expression
1		bj-hbaeb2	$$⊢\forall xx=y\leftrightarrow \forall x\forall zx=y$$
2		alcom	$$⊢\forall x\forall zx=y\leftrightarrow \forall z\forall xx=y$$
3	1 2	bitri	$$⊢\forall xx=y\leftrightarrow \forall z\forall xx=y$$