Theorem pm5.7

Description: Disjunction distributes over the biconditional. Theorem *5.7 of WhiteheadRussell p. 125. This theorem is similar to orbidi . (Contributed by Roy F. Longton, 21-Jun-2005)

	Ref	Expression
Assertion	pm5.7	|- ( ( ( ph \/ ch ) <-> ( ps \/ ch ) ) <-> ( ch \/ ( ph <-> ps ) ) )

Proof

Step	Hyp	Ref	Expression
1		orbidi	|- ( ( ch \/ ( ph <-> ps ) ) <-> ( ( ch \/ ph ) <-> ( ch \/ ps ) ) )
2		orcom	|- ( ( ch \/ ph ) <-> ( ph \/ ch ) )
3		orcom	|- ( ( ch \/ ps ) <-> ( ps \/ ch ) )
4	2 3	bibi12i	|- ( ( ( ch \/ ph ) <-> ( ch \/ ps ) ) <-> ( ( ph \/ ch ) <-> ( ps \/ ch ) ) )
5	1 4	bitr2i	|- ( ( ( ph \/ ch ) <-> ( ps \/ ch ) ) <-> ( ch \/ ( ph <-> ps ) ) )