Metamath Proof Explorer


Theorem oran

Description: Disjunction in terms of conjunction (De Morgan's law). Compare Theorem *4.57 of WhiteheadRussell p. 120. (Contributed by NM, 3-Jan-1993) (Proof shortened by Andrew Salmon, 7-May-2011)

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

Proof

Step Hyp Ref Expression
1 pm4.56
 |-  ( ( -. ph /\ -. ps ) <-> -. ( ph \/ ps ) )
2 1 con2bii
 |-  ( ( ph \/ ps ) <-> -. ( -. ph /\ -. ps ) )