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 ) ) |
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 ) ) |