Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
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 13370 | . 2 ⊢ (𝐴 ∈ ℝ → (⌊‘𝐴) ∈ ℤ) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (⌊‘𝐴) ∈ ℤ) |
Copyright terms: Public domain | W3C validator |