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Mirrors > Home > MPE Home > Th. List > zeo3 | Structured version Visualization version GIF version |
Description: An integer is even or odd. With this representation of even and odd integers, this variant of zeo 11339 follows immediatly from the law of excluded middle, see exmidd 431. (Contributed by AV, 17-Jun-2021.) |
Ref | Expression |
---|---|
zeo3 | ⊢ (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exmidd 431 | 1 ⊢ (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 382 ∈ wcel 1977 class class class wbr 4583 2c2 10947 ℤcz 11254 ∥ cdvds 14821 |
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 196 df-or 384 |
This theorem is referenced by: zeo5 14918 |
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