Theorem sqrtgt0i

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

	Ref	Expression
Hypothesis	sqrtthi.1	$$⊢A\in ℝ$$
Assertion	sqrtgt0i	$$⊢0<A\to 0<\sqrt{A}$$

Proof

Step	Hyp	Ref	Expression
1		sqrtthi.1	$$⊢A\in ℝ$$
2		sqrtgt0	$$⊢\left(A\in ℝ\wedge 0<A\right)\to 0<\sqrt{A}$$
3	1 2	mpan	$$⊢0<A\to 0<\sqrt{A}$$