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Theorem zeo4 16155
Description: An integer is even or odd but not both. With this representation of even and odd integers, this variant of zeo2 12521 follows immediately from the principle of double negation, see notnotb 315. (Contributed by AV, 17-Jun-2021.)
Assertion
Ref Expression
zeo4 (𝑁 ∈ ℤ → (2 ∥ 𝑁 ↔ ¬ ¬ 2 ∥ 𝑁))

Proof of Theorem zeo4
StepHypRef Expression
1 notnotb 315 . 2 (2 ∥ 𝑁 ↔ ¬ ¬ 2 ∥ 𝑁)
21a1i 11 1 (𝑁 ∈ ℤ → (2 ∥ 𝑁 ↔ ¬ ¬ 2 ∥ 𝑁))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wb 205  wcel 2107   class class class wbr 5104  2c2 12142  cz 12433  cdvds 16071
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
This theorem is referenced by: (None)
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