Theorem bj-bisym 32575

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

Assertion

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

Proof of Theorem bj-bisym

Step	Hyp	Ref	Expression
1		impbi 198	. 2 |- ( ( ch -> th ) -> ( ( th -> ch ) -> ( ch <-> th ) ) )
2	1	bj-bi3ant 32574	1 |- ( ( ( ph -> ps ) -> ( ch -> th ) ) -> ( ( ( ps -> ph ) -> ( th -> ch ) ) -> ( ( ph <-> ps ) -> ( ch <-> th ) ) ) )

Syntax hints:   -> wi 4   <-> wb 196

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 197

This theorem is referenced by: (None)