Metamath Proof Explorer

Theorem sqrtgt0d

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 sqrtgt0d 
|- ( ph -> 0 < ( sqrt ` A ) )

Proof

Step Hyp Ref Expression
1 sqrgt0d.1 
 |-  ( ph -> A e. RR+ )
2 1 rpsqrtcld 
 |-  ( ph -> ( sqrt ` A ) e. RR+ )
3 2 rpgt0d 
 |-  ( ph -> 0 < ( sqrt ` A ) )