Theorem orordir 691

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 674	. . 3 |- ( ( ch \/ ch ) <-> ch )
2	1	orbi2i 679	. 2 |- ( ( ( ph \/ ps ) \/ ( ch \/ ch ) ) <-> ( ( ph \/ ps ) \/ ch ) )
3		or4 688	. 2 |- ( ( ( ph \/ ps ) \/ ( ch \/ ch ) ) <-> ( ( ph \/ ch ) \/ ( ps \/ ch ) ) )
4	2, 3	bitr3i 175	1 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ( ph \/ ch ) \/ ( ps \/ ch ) ) )

Syntax hints:   <-> wb 98   \/ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  elznn0  8260