orddi - Metamath Proof Explorer

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Theorem orddi 913

Description: Double distributive law for disjunction. (Contributed by NM, 12-Aug-1994.)

**Assertion**
Ref	Expression
orddi	$/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$

**Proof of Theorem orddi**
Step	Hyp	Ref	Expression
1		ordir 909	. 2 $/\$ $\/$ $/\$ $\/$ $/\$ $/\$ $\/$ $/\$
2		ordi 908	. . 3 $\/$ $/\$ $\/$ $/\$ $\/$
3		ordi 908	. . 3 $\/$ $/\$ $\/$ $/\$ $\/$
4	2, 3	anbi12i 733	. 2 $\/$ $/\$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$
5	1, 4	bitri 264	1 $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$

Colors of variables: wff setvar class

Syntax hints:

wb 196 $\/$ wo 383 $/\$ wa 384

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 df-an 386

This theorem is referenced by: prneimg 4388 wl-cases2-dnf 33295