Theorem zeo3 16508

Description: An integer is even or odd. With this representation of even and odd integers, this variant of zeo 12786 follows immediately from the law of excluded middle, see exmidd 909. (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 909	1 ⊢ (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁))

This proof depends on syntax axioms:  ¬ wn 3   → wi 4   ∨ wo 861   ∈ wcel 2145   class class class wbr 5103  2c2 12398  ℤcz 12694   ∥ cdvds 16423

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862

This theorem is used by:  zeo5  16527