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Theorem wl-dfnan2 33267
Description: An alternative definition of "nand" based on imnan 438. See df-nan 1446 for the original definition. This theorem allows various shortenings. (Contributed by Wolf Lammen, 26-Jun-2020.)
Assertion
Ref Expression
wl-dfnan2 ((𝜑𝜓) ↔ (𝜑 → ¬ 𝜓))

Proof of Theorem wl-dfnan2
StepHypRef Expression
1 df-nan 1446 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
2 imnan 438 . 2 ((𝜑 → ¬ 𝜓) ↔ ¬ (𝜑𝜓))
31, 2bitr4i 267 1 ((𝜑𝜓) ↔ (𝜑 → ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 196  wa 384  wnan 1445
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 386  df-nan 1446
This theorem is referenced by:  wl-nancom  33268  wl-nannan  33269  wl-nannot  33270  wl-nanbi1  33271  wl-nanbi2  33272
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