MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  zeo3 Structured version   Visualization version   GIF version

Theorem zeo3 16154
Description: An integer is even or odd. With this representation of even and odd integers, this variant of zeo 12520 follows immediately from the law of excluded middle, see exmidd 895. (Contributed by AV, 17-Jun-2021.)
Assertion
Ref Expression
zeo3 (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁))

Proof of Theorem zeo3
StepHypRef Expression
1 exmidd 895 1 (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 846  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  df-or 847
This theorem is referenced by:  zeo5  16173
  Copyright terms: Public domain W3C validator