orordir - Metamath Proof Explorer

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Theorem orordir 553

Description: Distribution of disjunction over disjunction. (Contributed by NM, 25-Feb-1995.)

**Assertion**
Ref	Expression
orordir	$\/$ $\/$ $\/$ $\/$ $\/$

**Proof of Theorem orordir**
Step	Hyp	Ref	Expression
1		oridm 536	. . 3 $\/$
2	1	orbi2i 541	. 2 $\/$ $\/$ $\/$ $\/$ $\/$
3		or4 550	. 2 $\/$ $\/$ $\/$ $\/$ $\/$ $\/$
4	2, 3	bitr3i 266	1 $\/$ $\/$ $\/$ $\/$ $\/$

Colors of variables: wff setvar class

Syntax hints:

wb 196 $\/$ wo 383

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8

This theorem depends on definitions: df-bi 197 df-or 385

This theorem is referenced by: sspsstri 3709 psslinpr 9853 elznn0 11392 tosso 17036 legso 25494