Theorem ordir 596

Description: Distributive law for disjunction.

Assertion

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

Proof of Theorem ordir

Step	Hyp	Ref	Expression
1		ordi 595	. 2 |- ((ch \/ (ph /\ ps)) <-> ((ch \/ ph) /\ (ch \/ ps)))
2		orcom 246	. 2 |- (((ph /\ ps) \/ ch) <-> (ch \/ (ph /\ ps)))
3		orcom 246	. . 3 |- ((ph \/ ch) <-> (ch \/ ph))
4		orcom 246	. . 3 |- ((ps \/ ch) <-> (ch \/ ps))
5	3, 4	anbi12i 482	. 2 |- (((ph \/ ch) /\ (ps \/ ch)) <-> ((ch \/ ph) /\ (ch \/ ps)))
6	1, 2, 5	3bitr4 183	1 |- (((ph /\ ps) \/ ch) <-> ((ph \/ ch) /\ (ps \/ ch)))

Syntax hints:   <-> wb 146   \/ wo 222   /\ wa 223

This theorem is referenced by:  orddi 605  pm5.62 732  pwundif 2825  mapdom2 4487  elnn0z 6108

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  df-an 225

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