Metamath Proof Explorer

Theorem 1onn

Description: One is a natural number. (Contributed by NM, 29-Oct-1995)

Ref Expression
Assertion 1onn 
|- 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