Description: A weak universe containing _om contains the complex number construction. This theorem is construction-dependent in the literal sense, but will also be satisfied by any other reasonable implementation of the complex numbers. (Contributed by Mario Carneiro, 2-Jan-2017)
Ref | Expression | ||
---|---|---|---|
Hypotheses | wuncn.1 | |
|
wuncn.2 | |
||
Assertion | wuncn | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | wuncn.1 | |
|
2 | wuncn.2 | |
|
3 | df-c | |
|
4 | df-nr | |
|
5 | df-ni | |
|
6 | 1 2 | wundif | |
7 | 5 6 | eqeltrid | |
8 | 1 7 7 | wunxp | |
9 | elpqn | |
|
10 | 9 | ssriv | |
11 | 10 | a1i | |
12 | 1 8 11 | wunss | |
13 | 1 12 | wunpw | |
14 | prpssnq | |
|
15 | 14 | pssssd | |
16 | velpw | |
|
17 | 15 16 | sylibr | |
18 | 17 | ssriv | |
19 | 18 | a1i | |
20 | 1 13 19 | wunss | |
21 | 1 20 20 | wunxp | |
22 | 1 21 | wunpw | |
23 | enrer | |
|
24 | 23 | a1i | |
25 | 24 | qsss | |
26 | 1 22 25 | wunss | |
27 | 4 26 | eqeltrid | |
28 | 1 27 27 | wunxp | |
29 | 3 28 | eqeltrid | |