Theorem 2nn

Description: 2 is a positive integer. (Contributed by NM, 20-Aug-2001)

	Ref	Expression
Assertion	2nn	⊢ 2 ∈ ℕ

Proof

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