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 ∈ ℝ
Assertion	sqrtgt0i	⊢ ( 0 < 𝐴 → 0 < ( √ ‘ 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		sqrtthi.1	⊢ 𝐴 ∈ ℝ
2		sqrtgt0	⊢ ( ( 𝐴 ∈ ℝ ∧ 0 < 𝐴 ) → 0 < ( √ ‘ 𝐴 ) )
3	1 2	mpan	⊢ ( 0 < 𝐴 → 0 < ( √ ‘ 𝐴 ) )