Theorem bj-bisym

Description: This used to be in the main part. (Contributed by Wolf Lammen, 14-May-2013) (Revised by BJ, 14-Jun-2019)

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

Proof

Step	Hyp	Ref	Expression
1		impbi	|- ( ( ch -> th ) -> ( ( th -> ch ) -> ( ch <-> th ) ) )
2	1	bj-bi3ant	|- ( ( ( ph -> ps ) -> ( ch -> th ) ) -> ( ( ( ps -> ph ) -> ( th -> ch ) ) -> ( ( ph <-> ps ) -> ( ch <-> th ) ) ) )