| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > nn0p1nn | Structured version Visualization version GIF version | ||
| Description: A nonnegative integer plus 1 is a positive integer. Strengthening of peano2nn 12278. (Contributed by Raph Levien, 30-Jun-2006.) (Revised by Mario Carneiro, 16-May-2014.) |
| Ref | Expression |
|---|---|
| nn0p1nn | ⊢ (𝑁 ∈ ℕ0 → (𝑁 + 1) ∈ ℕ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 1nn 12277 | . 2 ⊢ 1 ∈ ℕ | |
| 2 | nn0nnaddcl 12557 | . 2 ⊢ ((𝑁 ∈ ℕ0 ∧ 1 ∈ ℕ) → (𝑁 + 1) ∈ ℕ) | |
| 3 | 1, 2 | mpan2 691 | 1 ⊢ (𝑁 ∈ ℕ0 → (𝑁 + 1) ∈ ℕ) |
| Copyright terms: Public domain | W3C validator |