Theorem imbi12d2a

Description: Variant of imbi12d2 . (Contributed by Zhi Wang, 30-Aug-2024)

	Ref	Expression
Hypotheses	imbi12d2.1	|- ( ph -> ( ps <-> ch ) )
	imbi12d2a.2	|- ( ( ph /\ ps ) -> ( th <-> ta ) )
Assertion	imbi12d2a	|- ( ph -> ( ( ps -> th ) <-> ( ch -> ta ) ) )

Proof

Step	Hyp	Ref	Expression
1		imbi12d2.1	|- ( ph -> ( ps <-> ch ) )
2		imbi12d2a.2	|- ( ( ph /\ ps ) -> ( th <-> ta ) )
3	2	ex	|- ( ph -> ( ps -> ( th <-> ta ) ) )
4	1 3	imbi12d2	|- ( ph -> ( ( ps -> th ) <-> ( ch -> ta ) ) )