Description: The imaginary part of a complex number representation. Definition 10-3.1 of Gleason p. 132. (Contributed by NM, 10-May-1999)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | crre.1 | |- A e. RR |
|
| crre.2 | |- B e. RR |
||
| Assertion | crimi | |- ( Im ` ( A + ( _i x. B ) ) ) = B |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | crre.1 | |- A e. RR |
|
| 2 | crre.2 | |- B e. RR |
|
| 3 | crim | |- ( ( A e. RR /\ B e. RR ) -> ( Im ` ( A + ( _i x. B ) ) ) = B ) |
|
| 4 | 1 2 3 | mp2an | |- ( Im ` ( A + ( _i x. B ) ) ) = B |