Theorem ordir

Description: Distributive law for disjunction. (Contributed by NM, 12-Aug-1994)

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

Proof

Step	Hyp	Ref	Expression
1		ordi	|- ( ( ch \/ ( ph /\ ps ) ) <-> ( ( ch \/ ph ) /\ ( ch \/ ps ) ) )
2		orcom	|- ( ( ( ph /\ ps ) \/ ch ) <-> ( ch \/ ( ph /\ ps ) ) )
3		orcom	|- ( ( ph \/ ch ) <-> ( ch \/ ph ) )
4		orcom	|- ( ( ps \/ ch ) <-> ( ch \/ ps ) )
5	3 4	anbi12i	|- ( ( ( ph \/ ch ) /\ ( ps \/ ch ) ) <-> ( ( ch \/ ph ) /\ ( ch \/ ps ) ) )
6	1 2 5	3bitr4i	|- ( ( ( ph /\ ps ) \/ ch ) <-> ( ( ph \/ ch ) /\ ( ps \/ ch ) ) )