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Theorem waj-ax 31018
 Description: A single axiom for propositional calculus offered by Wajsberg. (Contributed by Anthony Hart, 13-Aug-2011.)
Assertion
Ref Expression
waj-ax

Proof of Theorem waj-ax
StepHypRef Expression
1 nannan 1384 . . 3
2 simpr 462 . . . . . . . . 9
32imim2i 16 . . . . . . . 8
4 pm2.27 40 . . . . . . . . . 10
54anim2d 567 . . . . . . . . 9
65expdimp 438 . . . . . . . 8
73, 6syl5com 31 . . . . . . 7
87con3d 138 . . . . . 6
9 df-nan 1380 . . . . . 6
10 df-nan 1380 . . . . . 6
118, 9, 103imtr4g 273 . . . . 5
12 nanim 1386 . . . . 5
1311, 12sylib 199 . . . 4
14 pm3.21 449 . . . . . . . 8
1514adantr 466 . . . . . . 7
1615com12 32 . . . . . 6
1716a2i 14 . . . . 5
18 nannan 1384 . . . . 5
1917, 18sylibr 215 . . . 4
2013, 19jca 534 . . 3
211, 20sylbi 198 . 2
22 nannan 1384 . 2
2321, 22mpbir 212 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 370   wnan 1379 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-an 372  df-nan 1380 This theorem is referenced by: (None)
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