Theorem nn0ge0d

Description: A nonnegative integer is greater than or equal to zero. (Contributed by Mario Carneiro, 27-May-2016)

	Ref	Expression
Hypothesis	nn0red.1	⊢ ( 𝜑 → 𝐴 ∈ ℕ0 )
Assertion	nn0ge0d	⊢ ( 𝜑 → 0 ≤ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		nn0red.1	⊢ ( 𝜑 → 𝐴 ∈ ℕ0 )
2		nn0ge0	⊢ ( 𝐴 ∈ ℕ0 → 0 ≤ 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → 0 ≤ 𝐴 )