Theorem 4nn

Description: 4 is a positive integer. (Contributed by NM, 8-Jan-2006)

	Ref	Expression
Assertion	4nn	$$⊢4\in \mathbb{N}$$

Proof

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