Theorem 8onn

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

	Ref	Expression
Assertion	8onn	⊢ 8o ∈ ω

Proof

Step	Hyp	Ref	Expression
1		df-8o	⊢ 8o = suc 7o
2		7onn	⊢ 7o ∈ ω
3		peano2	⊢ ( 7o ∈ ω → suc 7o ∈ ω )
4	2 3	ax-mp	⊢ suc 7o ∈ ω
5	1 4	eqeltri	⊢ 8o ∈ ω