Theorem orordir 517

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

Assertion

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

Proof of Theorem orordir

Step	Hyp	Ref	Expression
1		oridm 500	. . 3 |- ((ch \/ ch) <-> ch)
2	1	orbi2i 505	. 2 |- (((ph \/ ps) \/ (ch \/ ch)) <-> ((ph \/ ps) \/ ch))
3		or4 514	. 2 |- (((ph \/ ps) \/ (ch \/ ch)) <-> ((ph \/ ch) \/ (ps \/ ch)))
4	2, 3	bitr3i 242	1 |- (((ph \/ ps) \/ ch) <-> ((ph \/ ch) \/ (ps \/ ch)))

Syntax hints:   <-> wb 176   \/ wo 357

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359

This theorem is referenced by:  sspsstri  3372