Metamath Proof Explorer


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+ )