![]() |
Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
|
Mirrors > Home > ILE Home > Th. List > df-met | Unicode version |
Description: Define the (proper) class of all metrics. (A metric space is the metric's base set paired with the metric. However, we will often also call the metric itself a "metric space".) Equivalent to Definition 14-1.1 of [Gleason] p. 223. (Contributed by NM, 25-Aug-2006.) |
Ref | Expression |
---|---|
df-met |
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cmet 13444 |
. 2
![]() ![]() | |
2 | vx |
. . 3
![]() ![]() | |
3 | cvv 2738 |
. . 3
![]() ![]() | |
4 | vy |
. . . . . . . . . . 11
![]() ![]() | |
5 | 4 | cv 1352 |
. . . . . . . . . 10
![]() ![]() |
6 | vz |
. . . . . . . . . . 11
![]() ![]() | |
7 | 6 | cv 1352 |
. . . . . . . . . 10
![]() ![]() |
8 | vd |
. . . . . . . . . . 11
![]() ![]() | |
9 | 8 | cv 1352 |
. . . . . . . . . 10
![]() ![]() |
10 | 5, 7, 9 | co 5875 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() |
11 | cc0 7811 |
. . . . . . . . 9
![]() ![]() | |
12 | 10, 11 | wceq 1353 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | 4, 6 | weq 1503 |
. . . . . . . 8
![]() ![]() ![]() ![]() |
14 | 12, 13 | wb 105 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | vw |
. . . . . . . . . . . 12
![]() ![]() | |
16 | 15 | cv 1352 |
. . . . . . . . . . 11
![]() ![]() |
17 | 16, 5, 9 | co 5875 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() |
18 | 16, 7, 9 | co 5875 |
. . . . . . . . . 10
![]() ![]() ![]() ![]() ![]() ![]() |
19 | caddc 7814 |
. . . . . . . . . 10
![]() ![]() | |
20 | 17, 18, 19 | co 5875 |
. . . . . . . . 9
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
21 | cle 7993 |
. . . . . . . . 9
![]() ![]() | |
22 | 10, 20, 21 | wbr 4004 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
23 | 2 | cv 1352 |
. . . . . . . 8
![]() ![]() |
24 | 22, 15, 23 | wral 2455 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
25 | 14, 24 | wa 104 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 25, 6, 23 | wral 2455 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
27 | 26, 4, 23 | wral 2455 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
28 | cr 7810 |
. . . . 5
![]() ![]() | |
29 | 23, 23 | cxp 4625 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() |
30 | cmap 6648 |
. . . . 5
![]() ![]() | |
31 | 28, 29, 30 | co 5875 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
32 | 27, 8, 31 | crab 2459 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
33 | 2, 3, 32 | cmpt 4065 |
. 2
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
34 | 1, 33 | wceq 1353 |
1
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Colors of variables: wff set class |
This definition is referenced by: metrel 13845 ismet 13847 |
Copyright terms: Public domain | W3C validator |