Theorem orordi 222

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 208	. . 3 |- ((ph \/ ph) <-> ph)
2	1	orbi1i 215	. 2 |- (((ph \/ ph) \/ (ps \/ ch)) <-> (ph \/ (ps \/ ch)))
3		or4 220	. 2 |- (((ph \/ ph) \/ (ps \/ ch)) <-> ((ph \/ ps) \/ (ph \/ ch)))
4	2, 3	bitr3 153	1 |- ((ph \/ (ps \/ ch)) <-> ((ph \/ ps) \/ (ph \/ ch)))

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

This theorem is referenced by:  pm2.85 439

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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