Metamath Proof Explorer

Theorem dfnan2

Description: Alternative denial in terms of our primitive connectives (implication and negation). (Contributed by WL, 26-Jun-2020)

Ref Expression
Assertion dfnan2 
|- ( ( ph -/\ ps ) <-> ( ph -> -. ps ) )

Proof

Step Hyp Ref Expression
1 df-nan 
 |-  ( ( ph -/\ ps ) <-> -. ( ph /\ ps ) )
2 imnan 
 |-  ( ( ph -> -. ps ) <-> -. ( ph /\ ps ) )
3 1 2 bitr4i 
 |-  ( ( ph -/\ ps ) <-> ( ph -> -. ps ) )