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| Mirrors > Home > MPE Home > Th. List > elfzelz | Structured version Visualization version GIF version | ||
| Description: A member of a finite set of sequential integers is an integer. (Contributed by NM, 6-Sep-2005.) (Revised by Mario Carneiro, 28-Apr-2015.) |
| Ref | Expression |
|---|---|
| elfzelz | ⊢ (𝐾 ∈ (𝑀...𝑁) → 𝐾 ∈ ℤ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elfzuz 13560 | . 2 ⊢ (𝐾 ∈ (𝑀...𝑁) → 𝐾 ∈ (ℤ≥‘𝑀)) | |
| 2 | eluzelz 12888 | . 2 ⊢ (𝐾 ∈ (ℤ≥‘𝑀) → 𝐾 ∈ ℤ) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝐾 ∈ (𝑀...𝑁) → 𝐾 ∈ ℤ) |
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