Theorem alexbii

Description: Biconditional form of aleximi . (Contributed by BJ, 16-Nov-2020)

	Ref	Expression
Hypothesis	alexbii.1	|- ( ph -> ( ps <-> ch ) )
Assertion	alexbii	|- ( A. x ph -> ( E. x ps <-> E. x ch ) )

Proof

Step	Hyp	Ref	Expression
1		alexbii.1	|- ( ph -> ( ps <-> ch ) )
2	1	biimpd	|- ( ph -> ( ps -> ch ) )
3	2	aleximi	|- ( A. x ph -> ( E. x ps -> E. x ch ) )
4	1	biimprd	|- ( ph -> ( ch -> ps ) )
5	4	aleximi	|- ( A. x ph -> ( E. x ch -> E. x ps ) )
6	3 5	impbid	|- ( A. x ph -> ( E. x ps <-> E. x ch ) )