Theorem 8nn

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

	Ref	Expression
Assertion	8nn	⊢ 8 ∈ ℕ

Proof

Step	Hyp	Ref	Expression
1		df-8	⊢ 8 = ( 7 + 1 )
2		7nn	⊢ 7 ∈ ℕ
3		peano2nn	⊢ ( 7 ∈ ℕ → ( 7 + 1 ) ∈ ℕ )
4	2 3	ax-mp	⊢ ( 7 + 1 ) ∈ ℕ
5	1 4	eqeltri	⊢ 8 ∈ ℕ