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Theorem nanan 1489
Description: Write 'and' in terms of 'nand'. (Contributed by Mario Carneiro, 9-May-2015.)
Assertion
Ref Expression
nanan ((𝜑𝜓) ↔ ¬ (𝜑𝜓))

Proof of Theorem nanan
StepHypRef Expression
1 df-nan 1488 . 2 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
21con2bii 346 1 ((𝜑𝜓) ↔ ¬ (𝜑𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wa 383  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-nan 1488
This theorem is referenced by:  nannan  1491  wl-nannan  33428
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