Theorem sqrtgt0ii

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
Hypotheses	sqrtthi.1	$$⊢A\in ℝ$$
	sqrpclii.2	$$⊢0<A$$
Assertion	sqrtgt0ii	$$⊢0<\sqrt{A}$$

Proof

Step	Hyp	Ref	Expression
1		sqrtthi.1	$$⊢A\in ℝ$$
2		sqrpclii.2	$$⊢0<A$$
3	1	sqrtgt0i	$$⊢0<A\to 0<\sqrt{A}$$
4	2 3	ax-mp	$$⊢0<\sqrt{A}$$