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Theorem nanor 1486
Description: Alternative denial in terms of disjunction and negation. This explains the name "alternative denial". (Contributed by BJ, 19-Oct-2022.)
Assertion
Ref Expression
nanor ((𝜑𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓))

Proof of Theorem nanor
StepHypRef Expression
1 df-nan 1483 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
2 ianor 979 . 2 (¬ (𝜑𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓))
31, 2bitri 278 1 ((𝜑𝜓) ↔ (¬ 𝜑 ∨ ¬ 𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 209  wa 399  wo 844  wnan 1482
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 210  df-an 400  df-or 845  df-nan 1483
This theorem is referenced by:  elnanelprv  32784  wl-df3maxtru1  34902
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