Theorem 8nn

Description: 8 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	8nn	$$⊢8\in \mathbb{N}$$

Proof

Step	Hyp	Ref	Expression
1		df-8	$$⊢8=7+1$$
2		7nn	$$⊢7\in \mathbb{N}$$
3		peano2nn	$$⊢7\in \mathbb{N}\to 7+1\in \mathbb{N}$$
4	2 3	ax-mp	$$⊢7+1\in \mathbb{N}$$
5	1 4	eqeltri	$$⊢8\in \mathbb{N}$$