Theorem 9nn

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

	Ref	Expression
Assertion	9nn	$$⊢9\in \mathbb{N}$$

Proof

Step	Hyp	Ref	Expression
1		df-9	$$⊢9=8+1$$
2		8nn	$$⊢8\in \mathbb{N}$$
3		peano2nn	$$⊢8\in \mathbb{N}\to 8+1\in \mathbb{N}$$
4	2 3	ax-mp	$$⊢8+1\in \mathbb{N}$$
5	1 4	eqeltri	$$⊢9\in \mathbb{N}$$