Metamath Proof Explorer

Theorem sqrtgt0i

Description: The square root of a positive real is positive. (Contributed by NM, 26-May-1999) (Revised by Mario Carneiro, 6-Sep-2013)

Ref Expression
Hypothesis sqrtthi.1 
|- A e. RR
Assertion sqrtgt0i 
|- ( 0 < A -> 0 < ( sqrt ` A ) )

Proof

Step Hyp Ref Expression
1 sqrtthi.1 
 |-  A e. RR
2 sqrtgt0 
 |-  ( ( A e. RR /\ 0 < A ) -> 0 < ( sqrt ` A ) )
3 1 2 mpan 
 |-  ( 0 < A -> 0 < ( sqrt ` A ) )