Metamath Proof Explorer

Theorem 4onn

Description: The ordinal 4 is a natural number. (Contributed by Mario Carneiro, 5-Jan-2016)

Ref Expression
Assertion 4onn 
|- 4o e. _om

Proof

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