Theorem zeo3 15678

Description: An integer is even or odd. With this representation of even and odd integers, this variant of zeo 12056 follows immediately from the law of excluded middle, see exmidd 893. (Contributed by AV, 17-Jun-2021.)

Assertion

Ref	Expression
zeo3	⊢ (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁))

Proof of Theorem zeo3

Step	Hyp	Ref	Expression
1		exmidd 893	1 ⊢ (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 844   ∈ wcel 2111   class class class wbr 5030  2c2 11680  ℤcz 11969   ∥ cdvds 15599

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 845

This theorem is referenced by:  zeo5  15697