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Theorem zeo3 16276
Description: An integer is even or odd. With this representation of even and odd integers, this variant of zeo 12644 follows immediately from the law of excluded middle, see exmidd 894. (Contributed by AV, 17-Jun-2021.)
Assertion
Ref Expression
zeo3 (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁))

Proof of Theorem zeo3
StepHypRef Expression
1 exmidd 894 1 (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 845  wcel 2106   class class class wbr 5147  2c2 12263  cz 12554  cdvds 16193
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 846
This theorem is referenced by:  zeo5  16295
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