Theorem 6nn

Description: 6 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	6nn	$$⊢6\in \mathbb{N}$$

Proof

Step	Hyp	Ref	Expression
1		df-6	$$⊢6=5+1$$
2		5nn	$$⊢5\in \mathbb{N}$$
3		peano2nn	$$⊢5\in \mathbb{N}\to 5+1\in \mathbb{N}$$
4	2 3	ax-mp	$$⊢5+1\in \mathbb{N}$$
5	1 4	eqeltri	$$⊢6\in \mathbb{N}$$