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Mirrors > Home > MPE Home > Th. List > df-sqrt | Structured version Visualization version Unicode version |
Description: Define a function whose
value is the square root of a complex number.
Since ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() See sqrtcl 13424 for its closure, sqrtval 13300 for its value, sqrtth 13427 and sqsqrti 13438 for its relationship to squares, and sqrt11i 13447 for uniqueness. (Contributed by NM, 27-Jul-1999.) (Revised by Mario Carneiro, 8-Jul-2013.) |
Ref | Expression |
---|---|
df-sqrt |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | csqrt 13296 |
. 2
![]() ![]() | |
2 | vx |
. . 3
![]() ![]() | |
3 | cc 9537 |
. . 3
![]() ![]() | |
4 | vy |
. . . . . . . 8
![]() ![]() | |
5 | 4 | cv 1443 |
. . . . . . 7
![]() ![]() |
6 | c2 10659 |
. . . . . . 7
![]() ![]() | |
7 | cexp 12272 |
. . . . . . 7
![]() ![]() | |
8 | 5, 6, 7 | co 6290 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() |
9 | 2 | cv 1443 |
. . . . . 6
![]() ![]() |
10 | 8, 9 | wceq 1444 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
11 | cc0 9539 |
. . . . . 6
![]() ![]() | |
12 | cre 13160 |
. . . . . . 7
![]() ![]() | |
13 | 5, 12 | cfv 5582 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() |
14 | cle 9676 |
. . . . . 6
![]() ![]() | |
15 | 11, 13, 14 | wbr 4402 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | ci 9541 |
. . . . . . 7
![]() ![]() | |
17 | cmul 9544 |
. . . . . . 7
![]() ![]() | |
18 | 16, 5, 17 | co 6290 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() |
19 | crp 11302 |
. . . . . 6
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20 | 18, 19 | wnel 2623 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | 10, 15, 20 | w3a 985 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
22 | 21, 4, 3 | crio 6251 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 2, 3, 22 | cmpt 4461 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | 1, 23 | wceq 1444 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff setvar class |
This definition is referenced by: sqrtval 13300 sqrtf 13426 |
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