Description: The real part of a number is less than or equal to its absolute value. Proposition 10-3.7(d) of Gleason p. 133. (Contributed by Mario Carneiro, 29-May-2016)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | abscld.1 | |- ( ph -> A e. CC ) |
|
| Assertion | releabsd | |- ( ph -> ( Re ` A ) <_ ( abs ` A ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | abscld.1 | |- ( ph -> A e. CC ) |
|
| 2 | releabs | |- ( A e. CC -> ( Re ` A ) <_ ( abs ` A ) ) |
|
| 3 | 1 2 | syl | |- ( ph -> ( Re ` A ) <_ ( abs ` A ) ) |