Description: Complex exponentiation of a quotient. (Contributed by Mario Carneiro, 8-Sep-2014)
Ref | Expression | ||
---|---|---|---|
Assertion | divcxp | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp1l | |
|
2 | simp1r | |
|
3 | simp2 | |
|
4 | 3 | rpreccld | |
5 | 4 | rpred | |
6 | 4 | rpge0d | |
7 | simp3 | |
|
8 | mulcxp | |
|
9 | 1 2 5 6 7 8 | syl221anc | |
10 | cxprec | |
|
11 | 3 7 10 | syl2anc | |
12 | 11 | oveq2d | |
13 | 9 12 | eqtrd | |
14 | 1 | recnd | |
15 | 3 | rpcnd | |
16 | 3 | rpne0d | |
17 | 14 15 16 | divrecd | |
18 | 17 | oveq1d | |
19 | cxpcl | |
|
20 | 14 7 19 | syl2anc | |
21 | cxpcl | |
|
22 | 15 7 21 | syl2anc | |
23 | cxpne0 | |
|
24 | 15 16 7 23 | syl3anc | |
25 | 20 22 24 | divrecd | |
26 | 13 18 25 | 3eqtr4d | |