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| Mirrors > Home > MPE Home > Th. List > resqcld | Structured version Visualization version GIF version | ||
| Description: Closure of squaring in reals, deduction form. (Contributed by Mario Carneiro, 28-May-2016.) |
| Ref | Expression |
|---|---|
| resqcld.1 | ⊢ (𝜑 → 𝐴 ∈ ℝ) |
| Ref | Expression |
|---|---|
| resqcld | ⊢ (𝜑 → (𝐴↑2) ∈ ℝ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | resqcld.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℝ) | |
| 2 | resqcl 14164 | . 2 ⊢ (𝐴 ∈ ℝ → (𝐴↑2) ∈ ℝ) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐴↑2) ∈ ℝ) |
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