Metamath Proof Explorer

Theorem biimpor

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

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

Proof

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