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Theorem anddi 816

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 814	. 2 $\/$ $/\$ $\/$ $/\$ $\/$ $\/$ $/\$ $\/$
2		andi 813	. . 3 $/\$ $\/$ $/\$ $\/$ $/\$
3		andi 813	. . 3 $/\$ $\/$ $/\$ $\/$ $/\$
4	2, 3	orbi12i 759	. 2 $/\$ $\/$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$
5	1, 4	bitri 183	1 $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$

Colors of variables: wff set class

Syntax hints: $/\$ wa 103

wb 104 $\/$ wo 703

This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 704

This theorem depends on definitions: df-bi 116

This theorem is referenced by: funun 5242 acexmidlemcase 5848 nnm00 6509