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Theorem wl-nannot 33429
Description: Show equivalence between negation and the Nicod version. To derive nic-dfneg 1635, apply nanbi 1494. (Contributed by Jeff Hoffman, 19-Nov-2007.) (Revised by Wolf Lammen, 26-Jun-2020.)
Assertion
Ref Expression
wl-nannot 𝜑 ↔ (𝜑𝜑))

Proof of Theorem wl-nannot
StepHypRef Expression
1 wl-dfnan2 33426 . 2 ((𝜑𝜑) ↔ (𝜑 → ¬ 𝜑))
2 pm4.8 379 . 2 ((𝜑 → ¬ 𝜑) ↔ ¬ 𝜑)
31, 2bitr2i 265 1 𝜑 ↔ (𝜑𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wnan 1487
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 197  df-an 385  df-nan 1488
This theorem is referenced by: (None)
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