Metamath Proof Explorer

Theorem notbinot1

Description: Simplification rule of negation across a biconditional. (Contributed by Giovanni Mascellani, 15-Sep-2017)

Ref Expression
Assertion notbinot1 
|- ( -. ( -. ph <-> ps ) <-> ( ph <-> ps ) )

Proof

Step Hyp Ref Expression
1 nbbn 
 |-  ( ( -. ph <-> ps ) <-> -. ( ph <-> ps ) )
2 1 bicomi 
 |-  ( -. ( ph <-> ps ) <-> ( -. ph <-> ps ) )
3 2 con1bii 
 |-  ( -. ( -. ph <-> ps ) <-> ( ph <-> ps ) )