anddi - Metamath Proof Explorer

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Theorem anddi 914

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

**Assertion**
Ref	Expression
anddi	$\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$

**Proof of Theorem anddi**
Step	Hyp	Ref	Expression
1		andir 912	. 2 $\/$ $/\$ $\/$ $/\$ $\/$ $\/$ $/\$ $\/$
2		andi 911	. . 3 $/\$ $\/$ $/\$ $\/$ $/\$
3		andi 911	. . 3 $/\$ $\/$ $/\$ $\/$ $/\$
4	2, 3	orbi12i 543	. 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: prnebg 4389 funun 5932 disjxpin 29401 icoreclin 33205 undif3VD 39118