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| Mirrors > Home > MPE Home > Th. List > eluzelz | Structured version Visualization version GIF version | ||
| Description: A member of an upper set of integers is an integer. (Contributed by NM, 6-Sep-2005.) |
| Ref | Expression |
|---|---|
| eluzelz | ⊢ (𝑁 ∈ (ℤ≥‘𝑀) → 𝑁 ∈ ℤ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | eluz2 12884 | . 2 ⊢ (𝑁 ∈ (ℤ≥‘𝑀) ↔ (𝑀 ∈ ℤ ∧ 𝑁 ∈ ℤ ∧ 𝑀 ≤ 𝑁)) | |
| 2 | 1 | simp2bi 1147 | 1 ⊢ (𝑁 ∈ (ℤ≥‘𝑀) → 𝑁 ∈ ℤ) |
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