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Theorem nannot 1450
Description: Show equivalence between negation and the Nicod version. To derive nic-dfneg 1592, apply nanbi 1451. (Contributed by Jeff Hoffman, 19-Nov-2007.)
Assertion
Ref Expression
nannot 𝜓 ↔ (𝜓𝜓))

Proof of Theorem nannot
StepHypRef Expression
1 df-nan 1445 . . 3 ((𝜓𝜓) ↔ ¬ (𝜓𝜓))
2 anidm 675 . . 3 ((𝜓𝜓) ↔ 𝜓)
31, 2xchbinx 324 . 2 ((𝜓𝜓) ↔ ¬ 𝜓)
43bicomi 214 1 𝜓 ↔ (𝜓𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 196  wa 384  wnan 1444
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 1445
This theorem is referenced by:  nanbi  1451  trunantru  1521  falnanfal  1524  nic-dfneg  1592  andnand1  32093  imnand2  32094
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