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

Theorem zeo3 15928
Description: An integer is even or odd. With this representation of even and odd integers, this variant of zeo 12290 follows immediately from the law of excluded middle, see exmidd 896. (Contributed by AV, 17-Jun-2021.)
Assertion
Ref Expression
zeo3 (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁))

Proof of Theorem zeo3
StepHypRef Expression
1 exmidd 896 1 (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  wo 847  wcel 2112   class class class wbr 5069  2c2 11912  cz 12203  cdvds 15845
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 210  df-or 848
This theorem is referenced by:  zeo5  15947
  Copyright terms: Public domain W3C validator