Metamath Proof Explorer


Theorem 9onn

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

Ref Expression
Assertion 9onn 9o ∈ ω

Proof

Step Hyp Ref Expression
1 df-9o ⊢ 9o = suc 8o
2 8onn ⊢ 8o ∈ ω
3 peano2 ⊢ ( 8o ∈ ω → suc 8o ∈ ω )
4 2 3 ax-mp ⊢ suc 8o ∈ ω
5 1 4 eqeltri ⊢ 9o ∈ ω