Theorem xrge0ge0

Description: A nonnegative extended real is nonnegative. (Contributed by Glauco Siliprandi, 11-Oct-2020)

	Ref	Expression
Assertion	xrge0ge0	⊢ ( 𝐴 ∈ ( 0 [,] +∞ ) → 0 ≤ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		elxrge0	⊢ ( 𝐴 ∈ ( 0 [,] +∞ ) ↔ ( 𝐴 ∈ ℝ* ∧ 0 ≤ 𝐴 ) )
2	1	biimpi	⊢ ( 𝐴 ∈ ( 0 [,] +∞ ) → ( 𝐴 ∈ ℝ* ∧ 0 ≤ 𝐴 ) )
3	2	simprd	⊢ ( 𝐴 ∈ ( 0 [,] +∞ ) → 0 ≤ 𝐴 )