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| Mirrors > Home > MPE Home > Th. List > renegcld | Structured version Visualization version GIF version | ||
| Description: Closure law for negative of reals. (Contributed by Mario Carneiro, 27-May-2016.) |
| Ref | Expression |
|---|---|
| renegcld.1 | ⊢ (𝜑 → 𝐴 ∈ ℝ) |
| Ref | Expression |
|---|---|
| renegcld | ⊢ (𝜑 → -𝐴 ∈ ℝ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | renegcld.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℝ) | |
| 2 | renegcl 11572 | . 2 ⊢ (𝐴 ∈ ℝ → -𝐴 ∈ ℝ) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → -𝐴 ∈ ℝ) |
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