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Theorem dn1 966
Description: A single axiom for Boolean algebra known as DN1. See http://www-unix.mcs.anl.gov/~mccune/papers/basax/v12.pdf. (Contributed by Jeff Hankins, 3-Jul-2009.) (Proof shortened by Andrew Salmon, 13-May-2011.) (Proof shortened by Wolf Lammen, 6-Jan-2013.)
Assertion
Ref Expression
dn1

Proof of Theorem dn1
StepHypRef Expression
1 pm2.45 397 . . . . 5
2 imnan 422 . . . . 5
31, 2mpbi 208 . . . 4
43biorfi 407 . . 3
5 orcom 387 . . . 4
6 ordir 865 . . . 4
75, 6bitri 249 . . 3
84, 7bitri 249 . 2
9 pm4.45 688 . . . . 5
10 anor 489 . . . . 5
119, 10bitri 249 . . . 4
1211orbi2i 519 . . 3
1312anbi2i 694 . 2
14 anor 489 . 2
158, 13, 143bitrri 272 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->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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