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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 12290 follows immediately from the law of excluded middle, see exmidd 896. (Contributed by AV, 17-Jun-2021.) |
Ref | Expression |
---|---|
zeo3 | ⊢ (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exmidd 896 | 1 ⊢ (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 847 ∈ wcel 2112 class class class wbr 5069 2c2 11912 ℤcz 12203 ∥ cdvds 15845 |
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 210 df-or 848 |
This theorem is referenced by: zeo5 15947 |
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