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| Mirrors > Home > MPE Home > Th. List > rge0ssre | Structured version Visualization version GIF version | ||
| Description: Nonnegative real numbers are real numbers. (Contributed by Thierry Arnoux, 9-Sep-2018.) (Proof shortened by AV, 8-Sep-2019.) |
| Ref | Expression |
|---|---|
| rge0ssre | ⊢ (0[,)+∞) ⊆ ℝ |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elrege0 13494 | . . 3 ⊢ (𝑥 ∈ (0[,)+∞) ↔ (𝑥 ∈ ℝ ∧ 0 ≤ 𝑥)) | |
| 2 | 1 | simplbi 497 | . 2 ⊢ (𝑥 ∈ (0[,)+∞) → 𝑥 ∈ ℝ) |
| 3 | 2 | ssriv 3987 | 1 ⊢ (0[,)+∞) ⊆ ℝ |
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