Metamath Proof Explorer

Theorem 3onn

Description: The ordinal 3 is a natural number. (Contributed by Mario Carneiro, 5-Jan-2016)

Ref Expression
Assertion 3onn 
|- 3o e. _om

Proof

Step Hyp Ref Expression
1 df-3o 
 |-  3o = suc 2o
2 2onn 
 |-  2o e. _om
3 peano2 
 |-  ( 2o e. _om -> suc 2o e. _om )
4 2 3 ax-mp 
 |-  suc 2o e. _om
5 1 4 eqeltri 
 |-  3o e. _om