Theorem 5nn

Description: 5 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	5nn	$$⊢5\in \mathbb{N}$$

Proof

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