Theorem notbinot1 33878

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

Assertion

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

Proof of Theorem notbinot1

Step	Hyp	Ref	Expression
1		nbbn 373	. . 3 |- ( ( -. ph <-> ps ) <-> -. ( ph <-> ps ) )
2	1	bicomi 214	. 2 |- ( -. ( ph <-> ps ) <-> ( -. ph <-> ps ) )
3	2	con1bii 346	1 |- ( -. ( -. ph <-> ps ) <-> ( ph <-> ps ) )

Syntax hints:   -. wn 3   <-> 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:  bicontr  33879