Theorem zeo3 16279

Description: An integer is even or odd. With this representation of even and odd integers, this variant of zeo 12646 follows immediately from the law of excluded middle, see exmidd 892. (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 892	1 ⊢ (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁))

Syntax hints:  ¬ wn 3   → wi 4   ∨ wo 844   ∈ wcel 2098   class class class wbr 5139  2c2 12265  ℤcz 12556   ∥ cdvds 16196

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 845

This theorem is referenced by:  zeo5  16298