Theorem imbibi

Description: The antecedent of one side of a biconditional can be moved out of the biconditional to become the antecedent of the remaining biconditional. (Contributed by BJ, 1-Jan-2025) (Proof shortened by Wolf Lammen, 5-Jan-2025) (Proof shortened by Garrett Katz, 15-Jun-2026)

	Ref	Expression
Assertion	imbibi	|- ( ( ( ph -> ps ) <-> ch ) -> ( ph -> ( ps <-> ch ) ) )

Proof

Step	Hyp	Ref	Expression
1		bitr3	|- ( ( ( ph -> ps ) <-> ps ) -> ( ( ( ph -> ps ) <-> ch ) -> ( ps <-> ch ) ) )
2		pm5.5	|- ( ph -> ( ( ph -> ps ) <-> ps ) )
3	1 2	syl11	|- ( ( ( ph -> ps ) <-> ch ) -> ( ph -> ( ps <-> ch ) ) )