Theorem rpsqrtcld

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

	Ref	Expression
Hypothesis	sqrgt0d.1	|- ( ph -> A e. RR+ )
Assertion	rpsqrtcld	|- ( ph -> ( sqrt ` A ) e. RR+ )

Proof

Step	Hyp	Ref	Expression
1		sqrgt0d.1	|- ( ph -> A e. RR+ )
2		rpsqrtcl	|- ( A e. RR+ -> ( sqrt ` A ) e. RR+ )
3	1 2	syl	|- ( ph -> ( sqrt ` A ) e. RR+ )