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Mirrors > Home > MPE Home > Th. List > resqcld | Structured version Visualization version GIF version |
Description: Closure of square in reals. (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 13582 | . 2 ⊢ (𝐴 ∈ ℝ → (𝐴↑2) ∈ ℝ) | |
3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐴↑2) ∈ ℝ) |
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