Theorem or4

Description: Rearrangement of 4 disjuncts. (Contributed by NM, 12-Aug-1994)

	Ref	Expression
Assertion	or4	|- ( ( ( ph \/ ps ) \/ ( ch \/ th ) ) <-> ( ( ph \/ ch ) \/ ( ps \/ th ) ) )

Proof

Step	Hyp	Ref	Expression
1		or12	|- ( ( ps \/ ( ch \/ th ) ) <-> ( ch \/ ( ps \/ th ) ) )
2	1	orbi2i	|- ( ( ph \/ ( ps \/ ( ch \/ th ) ) ) <-> ( ph \/ ( ch \/ ( ps \/ th ) ) ) )
3		orass	|- ( ( ( ph \/ ps ) \/ ( ch \/ th ) ) <-> ( ph \/ ( ps \/ ( ch \/ th ) ) ) )
4		orass	|- ( ( ( ph \/ ch ) \/ ( ps \/ th ) ) <-> ( ph \/ ( ch \/ ( ps \/ th ) ) ) )
5	2 3 4	3bitr4i	|- ( ( ( ph \/ ps ) \/ ( ch \/ th ) ) <-> ( ( ph \/ ch ) \/ ( ps \/ th ) ) )