Metamath Proof Explorer

Theorem nannot

Description: Negation in terms of alternative denial. (Contributed by Jeff Hoffman, 19-Nov-2007) (Revised by Wolf Lammen, 26-Jun-2020)

Ref Expression
Assertion nannot 
|- ( -. ph <-> ( ph -/\ ph ) )

Proof

Step Hyp Ref Expression
1 dfnan2 
 |-  ( ( ph -/\ ph ) <-> ( ph -> -. ph ) )
2 pm4.8 
 |-  ( ( ph -> -. ph ) <-> -. ph )
3 1 2 bitr2i 
 |-  ( -. ph <-> ( ph -/\ ph ) )