Theorem imbi12

Description: Closed form of imbi12i . Was automatically derived from its "Virtual Deduction" version and the Metamath program "MM-PA> MINIMIZE__WITH *" command. (Contributed by Alan Sare, 18-Mar-2012)

	Ref	Expression
Assertion	imbi12	|- ( ( ph <-> ps ) -> ( ( ch <-> th ) -> ( ( ph -> ch ) <-> ( ps -> th ) ) ) )

Proof

Step	Hyp	Ref	Expression
1		simplim	|- ( -. ( ( ph <-> ps ) -> -. ( ch <-> th ) ) -> ( ph <-> ps ) )
2		simprim	|- ( -. ( ( ph <-> ps ) -> -. ( ch <-> th ) ) -> ( ch <-> th ) )
3	1 2	imbi12d	|- ( -. ( ( ph <-> ps ) -> -. ( ch <-> th ) ) -> ( ( ph -> ch ) <-> ( ps -> th ) ) )
4	3	expi	|- ( ( ph <-> ps ) -> ( ( ch <-> th ) -> ( ( ph -> ch ) <-> ( ps -> th ) ) ) )