Theorem consensus 959

Description: The consensus theorem. This theorem and its dual (with \/ and /\ interchanged) are commonly used in computer logic design to eliminate redundant terms from Boolean expressions. Specifically, we prove that the term on the left-hand side is redundant. (Contributed by NM, 16-May-2003.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 20-Jan-2013.)

Assertion

Ref	Expression
consensus

Proof of Theorem consensus

Step	Hyp	Ref	Expression
1		id 22	. . 3
2		orc 385	. . . . 5
3	2	adantrr 716	. . . 4
4		olc 384	. . . . 5
5	4	adantrl 715	. . . 4
6	3, 5	pm2.61ian 790	. . 3
7	1, 6	jaoi 379	. 2
8		orc 385	. 2
9	7, 8	impbii 188	1

Syntax hints:  -.wn 3  <->wb 184  \/wo 368  /\wa 369

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