Theorem orordir

Description: Distribution of disjunction over disjunction. (Contributed by NM, 25-Feb-1995)

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

Proof

Step	Hyp	Ref	Expression
1		oridm	|- ( ( ch \/ ch ) <-> ch )
2	1	orbi2i	|- ( ( ( ph \/ ps ) \/ ( ch \/ ch ) ) <-> ( ( ph \/ ps ) \/ ch ) )
3		or4	|- ( ( ( ph \/ ps ) \/ ( ch \/ ch ) ) <-> ( ( ph \/ ch ) \/ ( ps \/ ch ) ) )
4	2 3	bitr3i	|- ( ( ( ph \/ ps ) \/ ch ) <-> ( ( ph \/ ch ) \/ ( ps \/ ch ) ) )