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Theorem nic-luk1 1524
Description: Proof of luk-1 1488 from nic-ax 1506 and nic-mp 1504 (and definitions nic-dfim 1502 and nic-dfneg 1503). Note that the standard axioms ax-1 6, ax-2 7, and ax-3 8 are proved from the Lukasiewicz axioms by theorems ax1 1499, ax2 1500, and ax3 1501. (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 1502 . . . 4
21nic-bi2 1522 . . 3
3 nic-ax 1506 . . . . . . 7
43nic-isw2 1514 . . . . . 6
54nic-idel 1517 . . . . 5
6 nic-dfim 1502 . . . . . . . . 9
76nic-bi1 1521 . . . . . . . 8
87nic-idbl 1519 . . . . . . 7
98nic-imp 1508 . . . . . 6
10 nic-dfim 1502 . . . . . . . . 9
1110nic-bi2 1522 . . . . . . . 8
12 nic-swap 1512 . . . . . . . 8
1311, 12nic-ich 1518 . . . . . . 7
1413nic-imp 1508 . . . . . 6
159, 14nic-ich 1518 . . . . 5
165, 15nic-ich 1518 . . . 4
17 nic-dfim 1502 . . . . 5
1817nic-bi1 1521 . . . 4
1916, 18nic-ich 1518 . . 3
202, 19nic-ich 1518 . 2
21 nic-dfim 1502 . . 3
2221nic-bi1 1521 . 2
2320, 22nic-mp 1504 1
Colors of variables: wff setvar class
Syntax hints:  ->wi 4  -/\wnan 1343
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 185  df-or 370  df-an 371  df-nan 1344
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