Metamath Proof Explorer


Theorem 1onnALT

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

Proof

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