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| Mirrors > Home > MPE Home > Th. List > flcld | Structured version Visualization version GIF version | ||
| Description: The floor (greatest integer) function is an integer (closure law). (Contributed by Mario Carneiro, 28-May-2016.) |
| Ref | Expression |
|---|---|
| flcld.1 | ⊢ (𝜑 → 𝐴 ∈ ℝ) |
| Ref | Expression |
|---|---|
| flcld | ⊢ (𝜑 → (⌊‘𝐴) ∈ ℤ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | flcld.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℝ) | |
| 2 | flcl 13835 | . 2 ⊢ (𝐴 ∈ ℝ → (⌊‘𝐴) ∈ ℤ) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (⌊‘𝐴) ∈ ℤ) |
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