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 NM, 2-Oct-1999)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | absvalsqi.1 | |- A e. CC |
|
| Assertion | releabsi | |- ( Re ` A ) <_ ( abs ` A ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | absvalsqi.1 | |- A e. CC |
|
| 2 | releabs | |- ( A e. CC -> ( Re ` A ) <_ ( abs ` A ) ) |
|
| 3 | 1 2 | ax-mp | |- ( Re ` A ) <_ ( abs ` A ) |