Theorem 4nn

Description: 4 is a positive integer. (Contributed by NM, 8-Jan-2006)

	Ref	Expression
Assertion	4nn	⊢ 4 ∈ ℕ

Proof

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