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Mirrors > Home > MPE Home > Th. List > ltaddrpd | Structured version Visualization version GIF version |
Description: Adding a positive number to another number increases it. (Contributed by Mario Carneiro, 28-May-2016.) |
Ref | Expression |
---|---|
rpgecld.1 | ⊢ (𝜑 → 𝐴 ∈ ℝ) |
rpgecld.2 | ⊢ (𝜑 → 𝐵 ∈ ℝ+) |
Ref | Expression |
---|---|
ltaddrpd | ⊢ (𝜑 → 𝐴 < (𝐴 + 𝐵)) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rpgecld.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℝ) | |
2 | rpgecld.2 | . 2 ⊢ (𝜑 → 𝐵 ∈ ℝ+) | |
3 | ltaddrp 11743 | . 2 ⊢ ((𝐴 ∈ ℝ ∧ 𝐵 ∈ ℝ+) → 𝐴 < (𝐴 + 𝐵)) | |
4 | 1, 2, 3 | syl2anc 691 | 1 ⊢ (𝜑 → 𝐴 < (𝐴 + 𝐵)) |
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