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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 13143 | . 2 ⊢ ((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ) → (𝐴[,]𝐵) ⊆ ℝ) | |
4 | 1, 2, 3 | syl2anc 583 | 1 ⊢ (𝜑 → (𝐴[,]𝐵) ⊆ ℝ) |
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