Theorem 9nn

Description: 9 is a positive integer. (Contributed by NM, 21-Oct-2012)

	Ref	Expression
Assertion	9nn	⊢ 9 ∈ ℕ

Proof

Step	Hyp	Ref	Expression
1		df-9	⊢ 9 = ( 8 + 1 )
2		8nn	⊢ 8 ∈ ℕ
3		peano2nn	⊢ ( 8 ∈ ℕ → ( 8 + 1 ) ∈ ℕ )
4	2 3	ax-mp	⊢ ( 8 + 1 ) ∈ ℕ
5	1 4	eqeltri	⊢ 9 ∈ ℕ