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Theorem dn1 974
 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 pm2.45 398 . . . . 5
2 imnan 423 . . . . 5
31, 2mpbi 211 . . . 4
43biorfi 408 . . 3
5 orcom 388 . . . 4
6 ordir 873 . . . 4
75, 6bitri 252 . . 3
84, 7bitri 252 . 2
9 pm4.45 692 . . . . 5
10 anor 491 . . . . 5
119, 10bitri 252 . . . 4
1211orbi2i 521 . . 3
1312anbi2i 698 . 2
14 anor 491 . 2
158, 13, 143bitrri 275 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 187   wo 369   wa 370 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 188  df-or 371  df-an 372 This theorem is referenced by: (None)
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