| Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
| Mirrors > Home > MPE Home > Th. List > 3pos | Structured version Visualization version GIF version | ||
| Description: The number 3 is positive. (Contributed by NM, 27-May-1999.) |
| Ref | Expression |
|---|---|
| 3pos | ⊢ 0 < 3 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | 2re 12340 | . . 3 ⊢ 2 ∈ ℝ | |
| 2 | 1re 11261 | . . 3 ⊢ 1 ∈ ℝ | |
| 3 | 2pos 12369 | . . 3 ⊢ 0 < 2 | |
| 4 | 0lt1 11785 | . . 3 ⊢ 0 < 1 | |
| 5 | 1, 2, 3, 4 | addgt0ii 11805 | . 2 ⊢ 0 < (2 + 1) |
| 6 | df-3 12330 | . 2 ⊢ 3 = (2 + 1) | |
| 7 | 5, 6 | breqtrri 5170 | 1 ⊢ 0 < 3 |
| Copyright terms: Public domain | W3C validator |