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| Mirrors > Home > MPE Home > Th. List > elrpd | Structured version Visualization version GIF version | ||
| Description: Membership in the set of positive reals. (Contributed by Mario Carneiro, 28-May-2016.) |
| Ref | Expression |
|---|---|
| elrpd.1 | ⊢ (𝜑 → 𝐴 ∈ ℝ) |
| elrpd.2 | ⊢ (𝜑 → 0 < 𝐴) |
| Ref | Expression |
|---|---|
| elrpd | ⊢ (𝜑 → 𝐴 ∈ ℝ+) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | elrpd.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℝ) | |
| 2 | elrpd.2 | . 2 ⊢ (𝜑 → 0 < 𝐴) | |
| 3 | elrp 13036 | . 2 ⊢ (𝐴 ∈ ℝ+ ↔ (𝐴 ∈ ℝ ∧ 0 < 𝐴)) | |
| 4 | 1, 2, 3 | sylanbrc 583 | 1 ⊢ (𝜑 → 𝐴 ∈ ℝ+) |
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