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Theorem nornot 1526
Description: ¬ is expressible via . (Contributed by Remi, 25-Oct-2023.) (Proof shortened by Wolf Lammen, 8-Dec-2023.)
Assertion
Ref Expression
nornot 𝜑 ↔ (𝜑 𝜑))

Proof of Theorem nornot
StepHypRef Expression
1 df-nor 1523 . . 3 ((𝜑 𝜑) ↔ ¬ (𝜑𝜑))
2 oridm 901 . . 3 ((𝜑𝜑) ↔ 𝜑)
31, 2xchbinx 333 . 2 ((𝜑 𝜑) ↔ ¬ 𝜑)
43bicomi 223 1 𝜑 ↔ (𝜑 𝜑))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wb 205  wo 843   wnor 1522
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 206  df-or 844  df-nor 1523
This theorem is referenced by:  noran  1528  noranOLD  1529  noror  1530  nororOLD  1531
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