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Mirrors > Home > MPE Home > Th. List > peano2re | Structured version Visualization version GIF version |
Description: A theorem for reals analogous the second Peano postulate peano2nn 11731. (Contributed by NM, 5-Jul-2005.) |
Ref | Expression |
---|---|
peano2re | ⊢ (𝐴 ∈ ℝ → (𝐴 + 1) ∈ ℝ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1re 10722 | . 2 ⊢ 1 ∈ ℝ | |
2 | readdcl 10701 | . 2 ⊢ ((𝐴 ∈ ℝ ∧ 1 ∈ ℝ) → (𝐴 + 1) ∈ ℝ) | |
3 | 1, 2 | mpan2 691 | 1 ⊢ (𝐴 ∈ ℝ → (𝐴 + 1) ∈ ℝ) |
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