Theorem sqrtge0i

Description: The square root of a nonnegative real is nonnegative. (Contributed by NM, 26-May-1999) (Revised by Mario Carneiro, 6-Sep-2013)

	Ref	Expression
Hypothesis	sqrtthi.1	$$⊢A\in ℝ$$
Assertion	sqrtge0i	$$⊢0\le A\to 0\le \sqrt{A}$$

Proof

Step	Hyp	Ref	Expression
1		sqrtthi.1	$$⊢A\in ℝ$$
2		sqrtge0	$$⊢\left(A\in ℝ\wedge 0\le A\right)\to 0\le \sqrt{A}$$
3	1 2	mpan	$$⊢0\le A\to 0\le \sqrt{A}$$