Detailed syntax breakdown of Definition df-cnext
Step | Hyp | Ref
| Expression |
1 | | ccnext 23210 |
. 2
class
CnExt |
2 | | vj |
. . 3
setvar 𝑗 |
3 | | vk |
. . 3
setvar 𝑘 |
4 | | ctop 22042 |
. . 3
class
Top |
5 | | vf |
. . . 4
setvar 𝑓 |
6 | 3 | cv 1538 |
. . . . . 6
class 𝑘 |
7 | 6 | cuni 4839 |
. . . . 5
class ∪ 𝑘 |
8 | 2 | cv 1538 |
. . . . . 6
class 𝑗 |
9 | 8 | cuni 4839 |
. . . . 5
class ∪ 𝑗 |
10 | | cpm 8616 |
. . . . 5
class
↑pm |
11 | 7, 9, 10 | co 7275 |
. . . 4
class (∪ 𝑘
↑pm ∪ 𝑗) |
12 | | vx |
. . . . 5
setvar 𝑥 |
13 | 5 | cv 1538 |
. . . . . . 7
class 𝑓 |
14 | 13 | cdm 5589 |
. . . . . 6
class dom 𝑓 |
15 | | ccl 22169 |
. . . . . . 7
class
cls |
16 | 8, 15 | cfv 6433 |
. . . . . 6
class
(cls‘𝑗) |
17 | 14, 16 | cfv 6433 |
. . . . 5
class
((cls‘𝑗)‘dom 𝑓) |
18 | 12 | cv 1538 |
. . . . . . 7
class 𝑥 |
19 | 18 | csn 4561 |
. . . . . 6
class {𝑥} |
20 | | cnei 22248 |
. . . . . . . . . . 11
class
nei |
21 | 8, 20 | cfv 6433 |
. . . . . . . . . 10
class
(nei‘𝑗) |
22 | 19, 21 | cfv 6433 |
. . . . . . . . 9
class
((nei‘𝑗)‘{𝑥}) |
23 | | crest 17131 |
. . . . . . . . 9
class
↾t |
24 | 22, 14, 23 | co 7275 |
. . . . . . . 8
class
(((nei‘𝑗)‘{𝑥}) ↾t dom 𝑓) |
25 | | cflf 23086 |
. . . . . . . 8
class
fLimf |
26 | 6, 24, 25 | co 7275 |
. . . . . . 7
class (𝑘 fLimf (((nei‘𝑗)‘{𝑥}) ↾t dom 𝑓)) |
27 | 13, 26 | cfv 6433 |
. . . . . 6
class ((𝑘 fLimf (((nei‘𝑗)‘{𝑥}) ↾t dom 𝑓))‘𝑓) |
28 | 19, 27 | cxp 5587 |
. . . . 5
class ({𝑥} × ((𝑘 fLimf (((nei‘𝑗)‘{𝑥}) ↾t dom 𝑓))‘𝑓)) |
29 | 12, 17, 28 | ciun 4924 |
. . . 4
class ∪ 𝑥 ∈ ((cls‘𝑗)‘dom 𝑓)({𝑥} × ((𝑘 fLimf (((nei‘𝑗)‘{𝑥}) ↾t dom 𝑓))‘𝑓)) |
30 | 5, 11, 29 | cmpt 5157 |
. . 3
class (𝑓 ∈ (∪ 𝑘
↑pm ∪ 𝑗) ↦ ∪
𝑥 ∈ ((cls‘𝑗)‘dom 𝑓)({𝑥} × ((𝑘 fLimf (((nei‘𝑗)‘{𝑥}) ↾t dom 𝑓))‘𝑓))) |
31 | 2, 3, 4, 4, 30 | cmpo 7277 |
. 2
class (𝑗 ∈ Top, 𝑘 ∈ Top ↦ (𝑓 ∈ (∪ 𝑘 ↑pm ∪ 𝑗)
↦ ∪ 𝑥 ∈ ((cls‘𝑗)‘dom 𝑓)({𝑥} × ((𝑘 fLimf (((nei‘𝑗)‘{𝑥}) ↾t dom 𝑓))‘𝑓)))) |
32 | 1, 31 | wceq 1539 |
1
wff CnExt =
(𝑗 ∈ Top, 𝑘 ∈ Top ↦ (𝑓 ∈ (∪ 𝑘
↑pm ∪ 𝑗) ↦ ∪
𝑥 ∈ ((cls‘𝑗)‘dom 𝑓)({𝑥} × ((𝑘 fLimf (((nei‘𝑗)‘{𝑥}) ↾t dom 𝑓))‘𝑓)))) |