Theorem 7nn

Description: 7 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	7nn	$$⊢7\in \mathbb{N}$$

Proof

Step	Hyp	Ref	Expression
1		df-7	$$⊢7=6+1$$
2		6nn	$$⊢6\in \mathbb{N}$$
3		peano2nn	$$⊢6\in \mathbb{N}\to 6+1\in \mathbb{N}$$
4	2 3	ax-mp	$$⊢6+1\in \mathbb{N}$$
5	1 4	eqeltri	$$⊢7\in \mathbb{N}$$