Metamath Proof Explorer

Theorem imnan

Description: Express an implication in terms of a negated conjunction. (Contributed by NM, 9-Apr-1994)

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

Proof

Step Hyp Ref Expression
1 df-an 
 |-  ( ( ph /\ ps ) <-> -. ( ph -> -. ps ) )
2 1 con2bii 
 |-  ( ( ph -> -. ps ) <-> -. ( ph /\ ps ) )