Theorem orordi 266

Description: Distribution of disjunction over disjunction.

Assertion

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

Proof of Theorem orordi

Step	Hyp	Ref	Expression
1		oridm 243	. . 3 |- ((ph \/ ph) <-> ph)
2	1	orbi1i 256	. 2 |- (((ph \/ ph) \/ (ps \/ ch)) <-> (ph \/ (ps \/ ch)))
3		or4 264	. 2 |- (((ph \/ ph) \/ (ps \/ ch)) <-> ((ph \/ ps) \/ (ph \/ ch)))
4	2, 3	bitr3 175	1 |- ((ph \/ (ps \/ ch)) <-> ((ph \/ ps) \/ (ph \/ ch)))

Syntax hints:   <-> wb 146   \/ wo 222

This theorem is referenced by:  pm2.85 581

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224

Copyright terms: Public domain