Theorem zeo3

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

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

Proof

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