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Theorem nic-luk1 1570
 Description: Proof of luk-1 1534 from nic-ax 1552 and nic-mp 1550 (and definitions nic-dfim 1548 and nic-dfneg 1549). Note that the standard axioms ax-1 6, ax-2 7, and ax-3 8 are proved from the Lukasiewicz axioms by theorems ax1 1545, ax2 1546, and ax3 1547. (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 1548 . . . 4
21nic-bi2 1568 . . 3
3 nic-ax 1552 . . . . . . 7
43nic-isw2 1560 . . . . . 6
54nic-idel 1563 . . . . 5
6 nic-dfim 1548 . . . . . . . . 9
76nic-bi1 1567 . . . . . . . 8
87nic-idbl 1565 . . . . . . 7
98nic-imp 1554 . . . . . 6
10 nic-dfim 1548 . . . . . . . . 9
1110nic-bi2 1568 . . . . . . . 8
12 nic-swap 1558 . . . . . . . 8
1311, 12nic-ich 1564 . . . . . . 7
1413nic-imp 1554 . . . . . 6
159, 14nic-ich 1564 . . . . 5
165, 15nic-ich 1564 . . . 4
17 nic-dfim 1548 . . . . 5
1817nic-bi1 1567 . . . 4
1916, 18nic-ich 1564 . . 3
202, 19nic-ich 1564 . 2
21 nic-dfim 1548 . . 3
2221nic-bi1 1567 . 2
2320, 22nic-mp 1550 1
 Colors of variables: wff setvar class Syntax hints:   wi 4   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-or 371  df-an 372  df-nan 1380 This theorem is referenced by: (None)
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