Theorem orordir 223

Description: Distribution of disjunction over disjunction.

Assertion

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

Proof of Theorem orordir

Step	Hyp	Ref	Expression
1		oridm 208	. . 3 |- ((ch \/ ch) <-> ch)
2	1	orbi2i 214	. 2 |- (((ph \/ ps) \/ (ch \/ ch)) <-> ((ph \/ ps) \/ ch))
3		or4 220	. 2 |- (((ph \/ ps) \/ (ch \/ ch)) <-> ((ph \/ ch) \/ (ps \/ ch)))
4	2, 3	bitr3 153	1 |- (((ph \/ ps) \/ ch) <-> ((ph \/ ch) \/ (ps \/ ch)))

Syntax hints:   <-> wb 127   \/ wo 195

This theorem is referenced by:  sspsstri 1572  psslinpr 3929  elznn0 4576

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-or 197

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