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Theorem dn1 933
 Description: A single axiom for Boolean algebra known as DN1. See http://www-unix.mcs.anl.gov/~mccune/papers/basax/v12.pdf. (Contributed by Jeffrey 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 pm2.45 387 . . . . 5
2 imnan 412 . . . . 5
31, 2mpbi 200 . . . 4
43biorfi 397 . . 3
5 orcom 377 . . . 4
6 ordir 836 . . . 4
75, 6bitri 241 . . 3
84, 7bitri 241 . 2
9 pm4.45 670 . . . . 5
10 anor 476 . . . . 5
119, 10bitri 241 . . . 4
1211orbi2i 506 . . 3
1312anbi2i 676 . 2
14 anor 476 . 2
158, 13, 143bitrri 264 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wb 177   wo 358   wa 359 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361
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