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Theorem nannot 1496
Description: Negation in terms of alternative denial. (Contributed by Jeff Hoffman, 19-Nov-2007.) (Revised by Wolf Lammen, 26-Jun-2020.)
Assertion
Ref Expression
nannot 𝜑 ↔ (𝜑𝜑))

Proof of Theorem nannot
StepHypRef Expression
1 dfnan2 1491 . 2 ((𝜑𝜑) ↔ (𝜑 → ¬ 𝜑))
2 pm4.8 392 . 2 ((𝜑 → ¬ 𝜑) ↔ ¬ 𝜑)
31, 2bitr2i 276 1 𝜑 ↔ (𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 206  wnan 1488
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 207  df-an 396  df-nan 1489
This theorem is referenced by:  nanbi  1497  trunantru  1578  falnanfal  1581  nic-dfneg  1668  andnand1  36367  imnand2  36368
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