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| Mirrors > Home > MPE Home > Th. List > elfzelzd | Structured version Visualization version GIF version | ||
| Description: A member of a finite set of sequential integers is an integer. (Contributed by Glauco Siliprandi, 5-Apr-2020.) |
| Ref | Expression |
|---|---|
| elfzelzd.1 | ⊢ (𝜑 → 𝐾 ∈ (𝑀...𝑁)) |
| Ref | Expression |
|---|---|
| elfzelzd | ⊢ (𝜑 → 𝐾 ∈ ℤ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elfzelzd.1 | . 2 ⊢ (𝜑 → 𝐾 ∈ (𝑀...𝑁)) | |
| 2 | elfzelz 13564 | . 2 ⊢ (𝐾 ∈ (𝑀...𝑁) → 𝐾 ∈ ℤ) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → 𝐾 ∈ ℤ) |
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