Description: A real number equals its real part. One direction of Proposition 10-3.4(f) of Gleason p. 133. (Contributed by Mario Carneiro, 29-May-2016)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | crred.1 | |- ( ph -> A e. RR ) |
|
| Assertion | rered | |- ( ph -> ( Re ` A ) = A ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | crred.1 | |- ( ph -> A e. RR ) |
|
| 2 | rere | |- ( A e. RR -> ( Re ` A ) = A ) |
|
| 3 | 1 2 | syl | |- ( ph -> ( Re ` A ) = A ) |