Theorem anddi 870

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 868	. 2
2		andi 867	. . 3
3		andi 867	. . 3
4	2, 3	orbi12i 521	. 2
5	1, 4	bitri 249	1

Syntax hints:  <->wb 184  \/wo 368  /\wa 369

This theorem is referenced by:  prnebg  4212  funun  5635  disjxpin  27447  undif3VD  33682

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 185  df-or 370  df-an 371