Theorem biimpor 33883

Description: A rewriting rule for biimplication. (Contributed by Giovanni Mascellani, 15-Sep-2017.)

Assertion

Ref	Expression
biimpor	|- ( ( ( ph <-> ps ) -> ch ) <-> ( ( -. ph <-> ps ) \/ ch ) )

Proof of Theorem biimpor

Step	Hyp	Ref	Expression
1		imor 428	. 2 |- ( ( ( ph <-> ps ) -> ch ) <-> ( -. ( ph <-> ps ) \/ ch ) )
2		notbinot2 33882	. . 3 |- ( -. ( ph <-> ps ) <-> ( -. ph <-> ps ) )
3	2	orbi1i 542	. 2 |- ( ( -. ( ph <-> ps ) \/ ch ) <-> ( ( -. ph <-> ps ) \/ ch ) )
4	1, 3	bitri 264	1 |- ( ( ( ph <-> ps ) -> ch ) <-> ( ( -. ph <-> ps ) \/ ch ) )

Syntax hints:   -. wn 3   -> wi 4   <-> wb 196   \/ wo 383

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  df-or 385

This theorem is referenced by: (None)