Metamath Proof Explorer

Theorem 8onn

Description: The ordinal 8 is a natural number. (Contributed by BTernaryTau, 4-Sep-2026)

Ref Expression
Assertion 8onn 
|- 8o e. _om

Proof

Step Hyp Ref Expression
1 df-8o 
 |-  8o = suc 7o
2 7onn 
 |-  7o e. _om
3 peano2 
 |-  ( 7o e. _om -> suc 7o e. _om )
4 2 3 ax-mp 
 |-  suc 7o e. _om
5 1 4 eqeltri 
 |-  8o e. _om