Theorem sqrtgt0d

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

	Ref	Expression
Hypothesis	sqrgt0d.1	$$⊢\phi \to A\in {ℝ}^{+}$$
Assertion	sqrtgt0d	$$⊢\phi \to 0<\sqrt{A}$$

Proof

Step	Hyp	Ref	Expression
1		sqrgt0d.1	$$⊢\phi \to A\in {ℝ}^{+}$$
2	1	rpsqrtcld	$$⊢\phi \to \sqrt{A}\in {ℝ}^{+}$$
3	2	rpgt0d	$$⊢\phi \to 0<\sqrt{A}$$