Description: Shorter proof of 1onn using Peano's postulates that depends on ax-un . (Contributed by NM, 29-Oct-1995) (Proof modification is discouraged.) (New usage is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Assertion | 1onnALT | |- 1o e. _om |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-1o | |- 1o = suc (/) |
|
| 2 | peano1 | |- (/) e. _om |
|
| 3 | peano2 | |- ( (/) e. _om -> suc (/) e. _om ) |
|
| 4 | 2 3 | ax-mp | |- suc (/) e. _om |
| 5 | 1 4 | eqeltri | |- 1o e. _om |