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Theorem nic-luk2 1457
 Description: Proof of luk-2 1421 from nic-ax 1438 and nic-mp 1436. (Contributed by Jeff Hoffman, 18-Nov-2007.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nic-luk2 ((¬ φφ) → φ)

Proof of Theorem nic-luk2
StepHypRef Expression
1 nic-dfim 1434 . . . . 5 (((¬ φ (φ φ)) φφ)) (((¬ φ (φ φ)) φ (φ φ))) ((¬ φφ) φφ))))
21nic-bi2 1454 . . . 4 ((¬ φφ) ((¬ φ (φ φ)) φ (φ φ))))
3 nic-dfneg 1435 . . . . . 6 (((φ φ) ¬ φ) (((φ φ) (φ φ)) φ ¬ φ)))
4 nic-id 1443 . . . . . 6 ((φ φ) ((φ φ) (φ φ)))
53, 4nic-iimp1 1447 . . . . 5 ((φ φ) ((φ φ) ¬ φ))
65nic-isw2 1446 . . . 4 ((φ φ) φ (φ φ)))
72, 6nic-iimp1 1447 . . 3 ((φ φ) φφ))
87nic-isw1 1445 . 2 ((¬ φφ) (φ φ))
9 nic-dfim 1434 . . 3 ((((¬ φφ) (φ φ)) ((¬ φφ) → φ)) ((((¬ φφ) (φ φ)) ((¬ φφ) (φ φ))) (((¬ φφ) → φ) ((¬ φφ) → φ))))
109nic-bi1 1453 . 2 (((¬ φφ) (φ φ)) (((¬ φφ) → φ) ((¬ φφ) → φ)))
118, 10nic-mp 1436 1 ((¬ φφ) → φ)
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → 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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