Theorem orordir 786

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 769	. . 3 |- ( ( ch \/ ch ) <-> ch )
2	1	orbi2i 774	. 2 |- ( ( ( ph \/ ps ) \/ ( ch \/ ch ) ) <-> ( ( ph \/ ps ) \/ ch ) )
3		or4 783	. 2 |- ( ( ( ph \/ ps ) \/ ( ch \/ ch ) ) <-> ( ( ph \/ ch ) \/ ( ps \/ ch ) ) )
4	2, 3	bitr3i 186	1 |- ( ( ( ph \/ ps ) \/ ch ) <-> ( ( ph \/ ch ) \/ ( ps \/ ch ) ) )

This proof depends on syntax axioms:   <-> wb 105   \/ wo 720

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-io 721

This proof depends on definitions:  df-bi 117

This theorem is used by:  elznn0  9659