Metamath Proof Explorer

Theorem or12

Description: Swap two disjuncts. (Contributed by NM, 5-Aug-1993) (Proof shortened by Wolf Lammen, 14-Nov-2012)

Ref Expression
Assertion or12 
|- ( ( ph \/ ( ps \/ ch ) ) <-> ( ps \/ ( ph \/ ch ) ) )

Proof

Step Hyp Ref Expression
1 pm1.5 
 |-  ( ( ph \/ ( ps \/ ch ) ) -> ( ps \/ ( ph \/ ch ) ) )
2 pm1.5 
 |-  ( ( ps \/ ( ph \/ ch ) ) -> ( ph \/ ( ps \/ ch ) ) )
3 1 2 impbii 
 |-  ( ( ph \/ ( ps \/ ch ) ) <-> ( ps \/ ( ph \/ ch ) ) )