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+ ) |
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+ ) |