Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > df-add | Structured version Visualization version Unicode version |
Description: Define addition over complex numbers. (Contributed by NM, 28-May-1995.) (New usage is discouraged.) |
Ref | Expression |
---|---|
df-add |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | caddc 9939 | . 2 | |
2 | vx | . . . . . . 7 | |
3 | 2 | cv 1482 | . . . . . 6 |
4 | cc 9934 | . . . . . 6 | |
5 | 3, 4 | wcel 1990 | . . . . 5 |
6 | vy | . . . . . . 7 | |
7 | 6 | cv 1482 | . . . . . 6 |
8 | 7, 4 | wcel 1990 | . . . . 5 |
9 | 5, 8 | wa 384 | . . . 4 |
10 | vw | . . . . . . . . . . . . 13 | |
11 | 10 | cv 1482 | . . . . . . . . . . . 12 |
12 | vv | . . . . . . . . . . . . 13 | |
13 | 12 | cv 1482 | . . . . . . . . . . . 12 |
14 | 11, 13 | cop 4183 | . . . . . . . . . . 11 |
15 | 3, 14 | wceq 1483 | . . . . . . . . . 10 |
16 | vu | . . . . . . . . . . . . 13 | |
17 | 16 | cv 1482 | . . . . . . . . . . . 12 |
18 | vf | . . . . . . . . . . . . 13 | |
19 | 18 | cv 1482 | . . . . . . . . . . . 12 |
20 | 17, 19 | cop 4183 | . . . . . . . . . . 11 |
21 | 7, 20 | wceq 1483 | . . . . . . . . . 10 |
22 | 15, 21 | wa 384 | . . . . . . . . 9 |
23 | vz | . . . . . . . . . . 11 | |
24 | 23 | cv 1482 | . . . . . . . . . 10 |
25 | cplr 9691 | . . . . . . . . . . . 12 | |
26 | 11, 17, 25 | co 6650 | . . . . . . . . . . 11 |
27 | 13, 19, 25 | co 6650 | . . . . . . . . . . 11 |
28 | 26, 27 | cop 4183 | . . . . . . . . . 10 |
29 | 24, 28 | wceq 1483 | . . . . . . . . 9 |
30 | 22, 29 | wa 384 | . . . . . . . 8 |
31 | 30, 18 | wex 1704 | . . . . . . 7 |
32 | 31, 16 | wex 1704 | . . . . . 6 |
33 | 32, 12 | wex 1704 | . . . . 5 |
34 | 33, 10 | wex 1704 | . . . 4 |
35 | 9, 34 | wa 384 | . . 3 |
36 | 35, 2, 6, 23 | coprab 6651 | . 2 |
37 | 1, 36 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: addcnsr 9956 axaddf 9966 |
Copyright terms: Public domain | W3C validator |