Metamath Proof Explorer

Theorem 9onn

Description: The ordinal 9 is a natural number. (Contributed by BTernaryTau, 4-Sep-2026)

Ref Expression
Assertion 9onn 
|- 9o e. _om

Proof

Step Hyp Ref Expression
1 df-9o 
 |-  9o = suc 8o
2 8onn 
 |-  8o e. _om
3 peano2 
 |-  ( 8o e. _om -> suc 8o e. _om )
4 2 3 ax-mp 
 |-  suc 8o e. _om
5 1 4 eqeltri 
 |-  9o e. _om