Theorem logic1

Description: Distribution of implication over biconditional with replacement (deduction form). (Contributed by Zhi Wang, 30-Aug-2024)

	Ref	Expression
Hypotheses	pm4.71da.1	|- ( ph -> ( ps <-> ch ) )
	logic1.2	|- ( ph -> ( ps -> ( th <-> ta ) ) )
Assertion	logic1	|- ( ph -> ( ( ps -> th ) <-> ( ch -> ta ) ) )

Proof

Step	Hyp	Ref	Expression
1		pm4.71da.1	|- ( ph -> ( ps <-> ch ) )
2		logic1.2	|- ( ph -> ( ps -> ( th <-> ta ) ) )
3	2	pm5.74d	|- ( ph -> ( ( ps -> th ) <-> ( ps -> ta ) ) )
4	1	imbi1d	|- ( ph -> ( ( ps -> ta ) <-> ( ch -> ta ) ) )
5	3 4	bitrd	|- ( ph -> ( ( ps -> th ) <-> ( ch -> ta ) ) )