Description: A number plus its conjugate is twice its real part. Compare Proposition 10-3.4(h) of Gleason p. 133. (Contributed by Mario Carneiro, 29-May-2016)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | recld.1 | |- ( ph -> A e. CC ) |
|
| Assertion | addcjd | |- ( ph -> ( A + ( * ` A ) ) = ( 2 x. ( Re ` A ) ) ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | recld.1 | |- ( ph -> A e. CC ) |
|
| 2 | addcj | |- ( A e. CC -> ( A + ( * ` A ) ) = ( 2 x. ( Re ` A ) ) ) |
|
| 3 | 1 2 | syl | |- ( ph -> ( A + ( * ` A ) ) = ( 2 x. ( Re ` A ) ) ) |