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| Mirrors > Home > MPE Home > Th. List > abscld | Structured version Visualization version GIF version | ||
| Description: Real closure of absolute value. (Contributed by Mario Carneiro, 29-May-2016.) |
| Ref | Expression |
|---|---|
| abscld.1 | ⊢ (𝜑 → 𝐴 ∈ ℂ) |
| Ref | Expression |
|---|---|
| abscld | ⊢ (𝜑 → (abs‘𝐴) ∈ ℝ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | abscld.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℂ) | |
| 2 | abscl 15317 | . 2 ⊢ (𝐴 ∈ ℂ → (abs‘𝐴) ∈ ℝ) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (abs‘𝐴) ∈ ℝ) |
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