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| Mirrors > Home > MPE Home > Th. List > iccssred | Structured version Visualization version GIF version | ||
| Description: A closed real interval is a set of reals. (Contributed by Glauco Siliprandi, 11-Dec-2019.) | 
| Ref | Expression | 
|---|---|
| iccssred.1 | ⊢ (𝜑 → 𝐴 ∈ ℝ) | 
| iccssred.2 | ⊢ (𝜑 → 𝐵 ∈ ℝ) | 
| Ref | Expression | 
|---|---|
| iccssred | ⊢ (𝜑 → (𝐴[,]𝐵) ⊆ ℝ) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | iccssred.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℝ) | |
| 2 | iccssred.2 | . 2 ⊢ (𝜑 → 𝐵 ∈ ℝ) | |
| 3 | iccssre 13470 | . 2 ⊢ ((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ) → (𝐴[,]𝐵) ⊆ ℝ) | |
| 4 | 1, 2, 3 | syl2anc 584 | 1 ⊢ (𝜑 → (𝐴[,]𝐵) ⊆ ℝ) | 
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