anddi - Intuitionistic Logic Explorer

	Intuitionistic Logic Explorer		< Previous Next > Nearby theorems
Mirrors > Home > ILE Home > Th. List > anddi		Unicode version

Theorem anddi 734

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 732	. 2 $\/$ $/\$ $\/$ $/\$ $\/$ $\/$ $/\$ $\/$
2		andi 731	. . 3 $/\$ $\/$ $/\$ $\/$ $/\$
3		andi 731	. . 3 $/\$ $\/$ $/\$ $\/$ $/\$
4	2, 3	orbi12i 681	. 2 $/\$ $\/$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$
5	1, 4	bitri 173	1 $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$ $\/$ $/\$

Colors of variables: wff set class

Syntax hints: $/\$ wa 97

wb 98 $\/$ wo 629

This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630

This theorem depends on definitions: df-bi 110

This theorem is referenced by: funun 4944 acexmidlemcase 5507 nnm00 6102