Theorem rpsqrtcld

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	rpsqrtcld	$$⊢\phi \to \sqrt{A}\in {ℝ}^{+}$$

Proof

Step	Hyp	Ref	Expression
1		sqrgt0d.1	$$⊢\phi \to A\in {ℝ}^{+}$$
2		rpsqrtcl	$$⊢A\in {ℝ}^{+}\to \sqrt{A}\in {ℝ}^{+}$$
3	1 2	syl	$$⊢\phi \to \sqrt{A}\in {ℝ}^{+}$$