Metamath Proof Explorer

Theorem or32

Description: A rearrangement of disjuncts. (Contributed by NM, 18-Oct-1995) (Proof shortened by Andrew Salmon, 26-Jun-2011)

Ref Expression
Assertion or32 
|- ( ( ( ph \/ ps ) \/ ch ) <-> ( ( ph \/ ch ) \/ ps ) )

Proof

Step Hyp Ref Expression
1 orass 
 |-  ( ( ( ph \/ ps ) \/ ch ) <-> ( ph \/ ( ps \/ ch ) ) )
2 or12 
 |-  ( ( ph \/ ( ps \/ ch ) ) <-> ( ps \/ ( ph \/ ch ) ) )
3 orcom 
 |-  ( ( ps \/ ( ph \/ ch ) ) <-> ( ( ph \/ ch ) \/ ps ) )
4 1 2 3 3bitri 
 |-  ( ( ( ph \/ ps ) \/ ch ) <-> ( ( ph \/ ch ) \/ ps ) )