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Mirrors > Home > ILE Home > Th. List > readdcld | GIF version |
Description: Closure law for addition of reals. (Contributed by Mario Carneiro, 27-May-2016.) |
Ref | Expression |
---|---|
recnd.1 | ⊢ (𝜑 → 𝐴 ∈ ℝ) |
readdcld.2 | ⊢ (𝜑 → 𝐵 ∈ ℝ) |
Ref | Expression |
---|---|
readdcld | ⊢ (𝜑 → (𝐴 + 𝐵) ∈ ℝ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | recnd.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℝ) | |
2 | readdcld.2 | . 2 ⊢ (𝜑 → 𝐵 ∈ ℝ) | |
3 | readdcl 7858 | . 2 ⊢ ((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ) → (𝐴 + 𝐵) ∈ ℝ) | |
4 | 1, 2, 3 | syl2anc 409 | 1 ⊢ (𝜑 → (𝐴 + 𝐵) ∈ ℝ) |
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