Theorem imbi12d3

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

	Ref	Expression
Hypotheses	imbi12d2.1	|- ( ph -> ( ps <-> ch ) )
	imbi12d3.2	|- ( ph -> ( ( ps /\ ch ) -> ( th <-> ta ) ) )
Assertion	imbi12d3	|- ( ph -> ( ( ps -> th ) <-> ( ch -> ta ) ) )

Proof

Step	Hyp	Ref	Expression
1		imbi12d2.1	|- ( ph -> ( ps <-> ch ) )
2		imbi12d3.2	|- ( ph -> ( ( ps /\ ch ) -> ( th <-> ta ) ) )
3	1	pm4.71da	|- ( ph -> ( ps <-> ( ps /\ ch ) ) )
4	3 2	sylbid	|- ( ph -> ( ps -> ( th <-> ta ) ) )
5	1 4	imbi12d2	|- ( ph -> ( ( ps -> th ) <-> ( ch -> ta ) ) )