Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > MPE Home > Th. List > df-re | Structured version Visualization version Unicode version |
Description: Define a function whose value is the real part of a complex number. See reval 13846 for its value, recli 13907 for its closure, and replim 13856 for its use in decomposing a complex number. (Contributed by NM, 9-May-1999.) |
Ref | Expression |
---|---|
df-re |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cre 13837 | . 2 | |
2 | vx | . . 3 | |
3 | cc 9934 | . . 3 | |
4 | 2 | cv 1482 | . . . . 5 |
5 | ccj 13836 | . . . . . 6 | |
6 | 4, 5 | cfv 5888 | . . . . 5 |
7 | caddc 9939 | . . . . 5 | |
8 | 4, 6, 7 | co 6650 | . . . 4 |
9 | c2 11070 | . . . 4 | |
10 | cdiv 10684 | . . . 4 | |
11 | 8, 9, 10 | co 6650 | . . 3 |
12 | 2, 3, 11 | cmpt 4729 | . 2 |
13 | 1, 12 | wceq 1483 | 1 |
Colors of variables: wff setvar class |
This definition is referenced by: reval 13846 ref 13852 cnre2csqima 29957 |
Copyright terms: Public domain | W3C validator |