Metamath Proof Explorer

Theorem 3oran

Description: Triple disjunction in terms of triple conjunction. (Contributed by NM, 8-Oct-2012)

Ref Expression
Assertion 3oran 
|- ( ( ph \/ ps \/ ch ) <-> -. ( -. ph /\ -. ps /\ -. ch ) )

Proof

Step Hyp Ref Expression
1 3ioran 
 |-  ( -. ( ph \/ ps \/ ch ) <-> ( -. ph /\ -. ps /\ -. ch ) )
2 1 con1bii 
 |-  ( -. ( -. ph /\ -. ps /\ -. ch ) <-> ( ph \/ ps \/ ch ) )
3 2 bicomi 
 |-  ( ( ph \/ ps \/ ch ) <-> -. ( -. ph /\ -. ps /\ -. ch ) )