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 ) |