Theorem 5nn

Description: 5 is a positive integer. (Contributed by Mario Carneiro, 15-Sep-2013)

	Ref	Expression
Assertion	5nn	⊢ 5 ∈ ℕ

Proof

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