Description: Shorter proof of 2onn using Peano's postulates that depends on ax-un . (Contributed by NM, 28-Sep-2004) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | 2onnALT | |- 2o e. _om |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-2o | |- 2o = suc 1o |
|
| 2 | 1onn | |- 1o e. _om |
|
| 3 | peano2 | |- ( 1o e. _om -> suc 1o e. _om ) |
|
| 4 | 2 3 | ax-mp | |- suc 1o e. _om |
| 5 | 1 4 | eqeltri | |- 2o e. _om |