Description: Real part of a product. (Contributed by Mario Carneiro, 2-Aug-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | remul2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | recn | |
|
2 | remul | |
|
3 | 1 2 | sylan | |
4 | rere | |
|
5 | 4 | adantr | |
6 | 5 | oveq1d | |
7 | reim0 | |
|
8 | 7 | oveq1d | |
9 | imcl | |
|
10 | 9 | recnd | |
11 | 10 | mul02d | |
12 | 8 11 | sylan9eq | |
13 | 6 12 | oveq12d | |
14 | recl | |
|
15 | 14 | recnd | |
16 | mulcl | |
|
17 | 1 15 16 | syl2an | |
18 | 17 | subid1d | |
19 | 3 13 18 | 3eqtrd | |