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 ∈ ℝ
	sqrpclii.2	⊢ 0 < 𝐴
Assertion	sqrtgt0ii	⊢ 0 < ( √ ‘ 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		sqrtthi.1	⊢ 𝐴 ∈ ℝ
2		sqrpclii.2	⊢ 0 < 𝐴
3	1	sqrtgt0i	⊢ ( 0 < 𝐴 → 0 < ( √ ‘ 𝐴 ) )
4	2 3	ax-mp	⊢ 0 < ( √ ‘ 𝐴 )