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