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| Mirrors > Home > MPE Home > Th. List > peano2nnd | Structured version Visualization version GIF version | ||
| Description: Peano postulate: a successor of a positive integer is a positive integer. (Contributed by Mario Carneiro, 27-May-2016.) |
| Ref | Expression |
|---|---|
| nnred.1 | ⊢ (𝜑 → 𝐴 ∈ ℕ) |
| Ref | Expression |
|---|---|
| peano2nnd | ⊢ (𝜑 → (𝐴 + 1) ∈ ℕ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | nnred.1 | . 2 ⊢ (𝜑 → 𝐴 ∈ ℕ) | |
| 2 | peano2nn 12278 | . 2 ⊢ (𝐴 ∈ ℕ → (𝐴 + 1) ∈ ℕ) | |
| 3 | 1, 2 | syl 17 | 1 ⊢ (𝜑 → (𝐴 + 1) ∈ ℕ) |
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