Theorem 0nn0

Description: 0 is a nonnegative integer. (Contributed by Raph Levien, 10-Dec-2002)

	Ref	Expression
Assertion	0nn0	⊢ 0 ∈ ℕ0

Proof

Step	Hyp	Ref	Expression
1		eqid	⊢ 0 = 0
2		elnn0	⊢ ( 0 ∈ ℕ0 ↔ ( 0 ∈ ℕ ∨ 0 = 0 ) )
3	2	biimpri	⊢ ( ( 0 ∈ ℕ ∨ 0 = 0 ) → 0 ∈ ℕ0 )
4	3	olcs	⊢ ( 0 = 0 → 0 ∈ ℕ0 )
5	1 4	ax-mp	⊢ 0 ∈ ℕ0