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Theorem nic-luk3 1458
 Description: Proof of luk-3 1422 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-luk3 (φ → (¬ φψ))

Proof of Theorem nic-luk3
StepHypRef Expression
1 nic-dfim 1434 . . . 4 (((¬ φ (ψ ψ)) φψ)) (((¬ φ (ψ ψ)) φ (ψ ψ))) ((¬ φψ) φψ))))
21nic-bi1 1453 . . 3 ((¬ φ (ψ ψ)) ((¬ φψ) φψ)))
3 nic-dfneg 1435 . . . . 5 (((φ φ) ¬ φ) (((φ φ) (φ φ)) φ ¬ φ)))
43nic-bi2 1454 . . . 4 φ ((φ φ) (φ φ)))
5 nic-id 1443 . . . 4 (φ (φ φ))
64, 5nic-iimp1 1447 . . 3 (φ ¬ φ)
72, 6nic-iimp2 1448 . 2 (φ ((¬ φψ) φψ)))
8 nic-dfim 1434 . . 3 (((φ ((¬ φψ) φψ))) (φ → (¬ φψ))) (((φ ((¬ φψ) φψ))) (φ ((¬ φψ) φψ)))) ((φ → (¬ φψ)) (φ → (¬ φψ)))))
98nic-bi1 1453 . 2 ((φ ((¬ φψ) φψ))) ((φ → (¬ φψ)) (φ → (¬ φψ))))
107, 9nic-mp 1436 1 (φ → (¬ φψ))
 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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