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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 12644 follows immediately from the law of excluded middle, see exmidd 894. (Contributed by AV, 17-Jun-2021.) |
Ref | Expression |
---|---|
zeo3 | ⊢ (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | exmidd 894 | 1 ⊢ (𝑁 ∈ ℤ → (2 ∥ 𝑁 ∨ ¬ 2 ∥ 𝑁)) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 → wi 4 ∨ wo 845 ∈ wcel 2106 class class class wbr 5147 2c2 12263 ℤcz 12554 ∥ cdvds 16193 |
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 846 |
This theorem is referenced by: zeo5 16295 |
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