Theorem zeo3 16264

Description: An integer is even or odd. With this representation of even and odd integers, this variant of zeo 12578 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

Step	Hyp	Ref	Expression
1		exmidd 895	1 ⊢ (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 847   ∈ wcel 2113   class class class wbr 5098  2c2 12200  ℤcz 12488   ∥ cdvds 16179

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 207  df-or 848

This theorem is referenced by:  zeo5  16283