![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > MPE Home > Th. List > df-ply | Structured version Visualization version Unicode version |
Description: Define the set of polynomials on the complex numbers with coefficients in the given subset. (Contributed by Mario Carneiro, 17-Jul-2014.) |
Ref | Expression |
---|---|
df-ply |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cply 23186 |
. 2
![]() | |
2 | vx |
. . 3
![]() ![]() | |
3 | cc 9562 |
. . . 4
![]() ![]() | |
4 | 3 | cpw 3962 |
. . 3
![]() ![]() ![]() |
5 | vf |
. . . . . . . 8
![]() ![]() | |
6 | 5 | cv 1453 |
. . . . . . 7
![]() ![]() |
7 | vz |
. . . . . . . 8
![]() ![]() | |
8 | cc0 9564 |
. . . . . . . . . 10
![]() ![]() | |
9 | vn |
. . . . . . . . . . 11
![]() ![]() | |
10 | 9 | cv 1453 |
. . . . . . . . . 10
![]() ![]() |
11 | cfz 11812 |
. . . . . . . . . 10
![]() ![]() | |
12 | 8, 10, 11 | co 6314 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() |
13 | vk |
. . . . . . . . . . . 12
![]() ![]() | |
14 | 13 | cv 1453 |
. . . . . . . . . . 11
![]() ![]() |
15 | va |
. . . . . . . . . . . 12
![]() ![]() | |
16 | 15 | cv 1453 |
. . . . . . . . . . 11
![]() ![]() |
17 | 14, 16 | cfv 5600 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() |
18 | 7 | cv 1453 |
. . . . . . . . . . 11
![]() ![]() |
19 | cexp 12303 |
. . . . . . . . . . 11
![]() ![]() | |
20 | 18, 14, 19 | co 6314 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() |
21 | cmul 9569 |
. . . . . . . . . 10
![]() ![]() | |
22 | 17, 20, 21 | co 6314 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 12, 22, 13 | csu 13800 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 7, 3, 23 | cmpt 4474 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 6, 24 | wceq 1454 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 2 | cv 1453 |
. . . . . . . 8
![]() ![]() |
27 | 8 | csn 3979 |
. . . . . . . 8
![]() ![]() ![]() ![]() |
28 | 26, 27 | cun 3413 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
29 | cn0 10897 |
. . . . . . 7
![]() ![]() | |
30 | cmap 7497 |
. . . . . . 7
![]() ![]() | |
31 | 28, 29, 30 | co 6314 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | 25, 15, 31 | wrex 2749 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
33 | 32, 9, 29 | wrex 2749 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
34 | 33, 5 | cab 2447 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
35 | 2, 4, 34 | cmpt 4474 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
36 | 1, 35 | wceq 1454 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
This definition is referenced by: plyval 23195 plybss 23196 |
Copyright terms: Public domain | W3C validator |