Metamath Proof Explorer


Theorem nn0ge0i

Description: Nonnegative integers are nonnegative. (Contributed by Raph Levien, 10-Dec-2002)

Ref Expression
Hypothesis nn0ge0i.1 𝑁 ∈ ℕ0
Assertion nn0ge0i 0 ≤ 𝑁

Proof

Step Hyp Ref Expression
1 nn0ge0i.1 𝑁 ∈ ℕ0
2 nn0ge0 ( 𝑁 ∈ ℕ0 → 0 ≤ 𝑁 )
3 1 2 ax-mp 0 ≤ 𝑁