Description: A number is real iff it equals its complex conjugate. Proposition 10-3.4(f) of Gleason p. 133. (Contributed by NM, 11-Oct-1999)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | recl.1 | |- A e. CC |
|
| Assertion | cjrebi | |- ( A e. RR <-> ( * ` A ) = A ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | recl.1 | |- A e. CC |
|
| 2 | cjreb | |- ( A e. CC -> ( A e. RR <-> ( * ` A ) = A ) ) |
|
| 3 | 1 2 | ax-mp | |- ( A e. RR <-> ( * ` A ) = A ) |