Description: The real part of the square root function is nonnegative. (Contributed by Mario Carneiro, 29-May-2016)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | abscld.1 | |- ( ph -> A e. CC ) |
|
| Assertion | sqrtrege0d | |- ( ph -> 0 <_ ( Re ` ( sqrt ` A ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | abscld.1 | |- ( ph -> A e. CC ) |
|
| 2 | sqrtrege0 | |- ( A e. CC -> 0 <_ ( Re ` ( sqrt ` A ) ) ) |
|
| 3 | 1 2 | syl | |- ( ph -> 0 <_ ( Re ` ( sqrt ` A ) ) ) |