Metamath Proof Explorer

Theorem or42

Description: Rearrangement of 4 disjuncts. (Contributed by NM, 10-Jan-2005)

Ref Expression
Assertion or42 
|- ( ( ( ph \/ ps ) \/ ( ch \/ th ) ) <-> ( ( ph \/ ch ) \/ ( th \/ ps ) ) )

Proof

Step Hyp Ref Expression
1 or4 
 |-  ( ( ( ph \/ ps ) \/ ( ch \/ th ) ) <-> ( ( ph \/ ch ) \/ ( ps \/ th ) ) )
2 orcom 
 |-  ( ( ps \/ th ) <-> ( th \/ ps ) )
3 2 orbi2i 
 |-  ( ( ( ph \/ ch ) \/ ( ps \/ th ) ) <-> ( ( ph \/ ch ) \/ ( th \/ ps ) ) )
4 1 3 bitri 
 |-  ( ( ( ph \/ ps ) \/ ( ch \/ th ) ) <-> ( ( ph \/ ch ) \/ ( th \/ ps ) ) )