Metamath Proof Explorer

Theorem 7onn

Description: The ordinal 7 is a natural number. (Contributed by BTernaryTau, 4-Sep-2026)

Ref Expression
Assertion 7onn 
|- 7o e. _om

Proof

Step Hyp Ref Expression
1 df-7o 
 |-  7o = suc 6o
2 6onn 
 |-  6o e. _om
3 peano2 
 |-  ( 6o e. _om -> suc 6o e. _om )
4 2 3 ax-mp 
 |-  suc 6o e. _om
5 1 4 eqeltri 
 |-  7o e. _om