Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  nic-luk1 Structured version   Unicode version

Theorem nic-luk1 1465
 Description: Proof of luk-1 1429 from nic-ax 1447 and nic-mp 1445 (and definitions nic-dfim 1443 and nic-dfneg 1444). Note that the standard axioms ax-1 5, ax-2 6, and ax-3 7 are proved from the Lukasiewicz axioms by theorems ax1 1440, ax2 1441, and ax3 1442. (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 1443 . . . 4
21nic-bi2 1463 . . 3
3 nic-ax 1447 . . . . . . 7
43nic-isw2 1455 . . . . . 6
54nic-idel 1458 . . . . 5
6 nic-dfim 1443 . . . . . . . . 9
76nic-bi1 1462 . . . . . . . 8
87nic-idbl 1460 . . . . . . 7
98nic-imp 1449 . . . . . 6
10 nic-dfim 1443 . . . . . . . . 9
1110nic-bi2 1463 . . . . . . . 8
12 nic-swap 1453 . . . . . . . 8
1311, 12nic-ich 1459 . . . . . . 7
1413nic-imp 1449 . . . . . 6
159, 14nic-ich 1459 . . . . 5
165, 15nic-ich 1459 . . . 4
17 nic-dfim 1443 . . . . 5
1817nic-bi1 1462 . . . 4
1916, 18nic-ich 1459 . . 3
202, 19nic-ich 1459 . 2
21 nic-dfim 1443 . . 3
2221nic-bi1 1462 . 2
2320, 22nic-mp 1445 1
 Colors of variables: wff set class Syntax hints:   wi 4   wnan 1296 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8 This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-nan 1297
 Copyright terms: Public domain W3C validator