Theorem orordir 723

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 706	. . 3 |- ( ( ch \/ ch ) <-> ch )
2	1	orbi2i 711	. 2 |- ( ( ( ph \/ ps ) \/ ( ch \/ ch ) ) <-> ( ( ph \/ ps ) \/ ch ) )
3		or4 720	. 2 |- ( ( ( ph \/ ps ) \/ ( ch \/ ch ) ) <-> ( ( ph \/ ch ) \/ ( ps \/ ch ) ) )
4	2, 3	bitr3i 184	1 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ( ph \/ ch ) \/ ( ps \/ ch ) ) )

Syntax hints:   <-> wb 103   \/ wo 661

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-io 662

This theorem depends on definitions:  df-bi 115

This theorem is referenced by:  elznn0  8366