Metamath Proof Explorer

Theorem 5onn

Description: The ordinal 5 is a natural number. (Contributed by BTernaryTau, 4-Sep-2026)

Ref Expression
Assertion 5onn 
|- 5o e. _om

Proof

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