Metamath Proof Explorer


Theorem ianor

Description: Negated conjunction in terms of disjunction (De Morgan's law). Theorem *4.51 of WhiteheadRussell p. 120. (Contributed by NM, 14-May-1993) (Proof shortened by Andrew Salmon, 13-May-2011)

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

Proof

Step Hyp Ref Expression
1 imnan
 |-  ( ( ph -> -. ps ) <-> -. ( ph /\ ps ) )
2 pm4.62
 |-  ( ( ph -> -. ps ) <-> ( -. ph \/ -. ps ) )
3 1 2 bitr3i
 |-  ( -. ( ph /\ ps ) <-> ( -. ph \/ -. ps ) )