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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
StepHypRef Expression
1 id 22 . . 3
2 orc 385 . . . . 5
32adantrr 716 . . . 4
4 olc 384 . . . . 5
54adantrl 715 . . . 4
63, 5pm2.61ian 790 . . 3
71, 6jaoi 379 . 2
8 orc 385 . 2
97, 8impbii 188 1
 Colors of variables: wff setvar class 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
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