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Theorem lukshef-ax2 31074
 Description: A single axiom for propositional calculus offered by Lukasiewicz. (Contributed by Anthony Hart, 14-Aug-2011.)
Assertion
Ref Expression
lukshef-ax2

Proof of Theorem lukshef-ax2
StepHypRef Expression
1 nannan 1385 . . . 4
21biimpi 198 . . 3
3 simpr 463 . . . . 5
43imim2i 16 . . . 4
5 simpl 459 . . . . . 6
65imim2i 16 . . . . 5
7 pm2.27 41 . . . . . . 7
87anim2d 568 . . . . . 6
98expdimp 439 . . . . 5
106, 9syl5com 32 . . . 4
11 ancr 552 . . . . 5
1211anim1i 571 . . . 4
134, 10, 12syl2anc 666 . . 3
14 con3 140 . . . . 5
15 df-nan 1381 . . . . 5
16 df-nan 1381 . . . . 5
1714, 15, 163imtr4g 274 . . . 4
1817anim2i 572 . . 3
19 nannan 1385 . . . . 5
2019biimpri 210 . . . 4
21 nanim 1387 . . . . 5
2221biimpi 198 . . . 4
2320, 22anim12i 569 . . 3
242, 13, 18, 234syl 19 . 2
25 nannan 1385 . 2
2624, 25mpbir 213 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 371   wnan 1380 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 189  df-an 373  df-nan 1381 This theorem is referenced by: (None)
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