Theorem sqrtgt0d

Description: The square root of a positive real is positive. (Contributed by Mario Carneiro, 29-May-2016)

	Ref	Expression
Hypothesis	sqrgt0d.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
Assertion	sqrtgt0d	⊢ ( 𝜑 → 0 < ( √ ‘ 𝐴 ) )

Proof

Step	Hyp	Ref	Expression
1		sqrgt0d.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ+ )
2	1	rpsqrtcld	⊢ ( 𝜑 → ( √ ‘ 𝐴 ) ∈ ℝ+ )
3	2	rpgt0d	⊢ ( 𝜑 → 0 < ( √ ‘ 𝐴 ) )