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Theorem nic-luk1 1456
 Description: Proof of luk-1 1420 from nic-ax 1438 and nic-mp 1436 (and definitions nic-dfim 1434 and nic-dfneg 1435). Note that the standard axioms ax-1 6, ax-2 7, and ax-3 8 are proved from the Lukasiewicz axioms by theorems ax1 1431, ax2 1432, and ax3 1433. (Contributed by Jeff Hoffman, 18-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nic-luk1

Proof of Theorem nic-luk1
StepHypRef Expression
1 nic-dfim 1434 . . . 4
21nic-bi2 1454 . . 3
3 nic-ax 1438 . . . . . . 7
43nic-isw2 1446 . . . . . 6
54nic-idel 1449 . . . . 5
6 nic-dfim 1434 . . . . . . . . 9
76nic-bi1 1453 . . . . . . . 8
87nic-idbl 1451 . . . . . . 7
98nic-imp 1440 . . . . . 6
10 nic-dfim 1434 . . . . . . . . 9
1110nic-bi2 1454 . . . . . . . 8
12 nic-swap 1444 . . . . . . . 8
1311, 12nic-ich 1450 . . . . . . 7
1413nic-imp 1440 . . . . . 6
159, 14nic-ich 1450 . . . . 5
165, 15nic-ich 1450 . . . 4
17 nic-dfim 1434 . . . . 5
1817nic-bi1 1453 . . . 4
1916, 18nic-ich 1450 . . 3
202, 19nic-ich 1450 . 2
21 nic-dfim 1434 . . 3
2221nic-bi1 1453 . 2
2320, 22nic-mp 1436 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   wnan 1287 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 177  df-or 359  df-an 360  df-nan 1288 This theorem is referenced by: (None)
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