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 |