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| Mirrors > Home > MPE Home > Th. List > relogcld | Structured version Visualization version GIF version | ||
| Description: Closure of the natural logarithm function. (Contributed by Mario Carneiro, 29-May-2016.) |
| Ref | Expression |
|---|---|
| relogcld.1 | ⊢ (𝜑 → 𝐴 ∈ ℝ+) |
| Ref | Expression |
|---|---|
| relogcld | ⊢ (𝜑 → (log‘𝐴) ∈ ℝ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | relogcld.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℝ+) | |
| 2 | relogcl 26751 | . 2 ⊢ (𝐴 ∈ ℝ+ → (log‘𝐴) ∈ ℝ) | |
| 3 | 1, 2 | syl 18 | 1 ⊢ (𝜑 → (log‘𝐴) ∈ ℝ) |
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