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Theorem nic-dfneg 1435
 Description: Define negation in terms of 'nand'. Analogous to ((φ ⊼ φ) ↔ ¬ φ). In a pure (standalone) treatment of Nicod's axiom, this theorem would be changed to a definition (\$a statement). (Contributed by NM, 11-Dec-2008.) (Proof modification is discouraged.) (New usage is discouraged.)
Assertion
Ref Expression
nic-dfneg (((φ φ) ¬ φ) (((φ φ) (φ φ)) φ ¬ φ)))

Proof of Theorem nic-dfneg
StepHypRef Expression
1 nannot 1293 . . 3 φ ↔ (φ φ))
21bicomi 193 . 2 ((φ φ) ↔ ¬ φ)
3 nanbi 1294 . 2 (((φ φ) ↔ ¬ φ) ↔ (((φ φ) ¬ φ) (((φ φ) (φ φ)) φ ¬ φ))))
42, 3mpbi 199 1 (((φ φ) ¬ φ) (((φ φ) (φ φ)) φ ¬ φ)))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   ↔ wb 176   ⊼ wnan 1287 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 177  df-or 359  df-an 360  df-nan 1288 This theorem is referenced by:  nic-luk2  1457  nic-luk3  1458
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