Step | Hyp | Ref
| Expression |
1 | | cdv 14060 |
. 2
class
D |
2 | | vs |
. . 3
setvar π |
3 | | vf |
. . 3
setvar π |
4 | | cc 7808 |
. . . 4
class
β |
5 | 4 | cpw 3575 |
. . 3
class π«
β |
6 | 2 | cv 1352 |
. . . 4
class π |
7 | | cpm 6648 |
. . . 4
class
βpm |
8 | 4, 6, 7 | co 5874 |
. . 3
class (β
βpm π ) |
9 | | vx |
. . . 4
setvar π₯ |
10 | 3 | cv 1352 |
. . . . . 6
class π |
11 | 10 | cdm 4626 |
. . . . 5
class dom π |
12 | | cabs 11005 |
. . . . . . . . 9
class
abs |
13 | | cmin 8127 |
. . . . . . . . 9
class
β |
14 | 12, 13 | ccom 4630 |
. . . . . . . 8
class (abs
β β ) |
15 | | cmopn 13381 |
. . . . . . . 8
class
MetOpen |
16 | 14, 15 | cfv 5216 |
. . . . . . 7
class
(MetOpenβ(abs β β )) |
17 | | crest 12687 |
. . . . . . 7
class
βΎt |
18 | 16, 6, 17 | co 5874 |
. . . . . 6
class
((MetOpenβ(abs β β )) βΎt π ) |
19 | | cnt 13529 |
. . . . . 6
class
int |
20 | 18, 19 | cfv 5216 |
. . . . 5
class
(intβ((MetOpenβ(abs β β )) βΎt
π )) |
21 | 11, 20 | cfv 5216 |
. . . 4
class
((intβ((MetOpenβ(abs β β )) βΎt
π ))βdom π) |
22 | 9 | cv 1352 |
. . . . . 6
class π₯ |
23 | 22 | csn 3592 |
. . . . 5
class {π₯} |
24 | | vz |
. . . . . . 7
setvar π§ |
25 | | vw |
. . . . . . . . . 10
setvar π€ |
26 | 25 | cv 1352 |
. . . . . . . . 9
class π€ |
27 | | cap 8537 |
. . . . . . . . 9
class
# |
28 | 26, 22, 27 | wbr 4003 |
. . . . . . . 8
wff π€ # π₯ |
29 | 28, 25, 11 | crab 2459 |
. . . . . . 7
class {π€ β dom π β£ π€ # π₯} |
30 | 24 | cv 1352 |
. . . . . . . . . 10
class π§ |
31 | 30, 10 | cfv 5216 |
. . . . . . . . 9
class (πβπ§) |
32 | 22, 10 | cfv 5216 |
. . . . . . . . 9
class (πβπ₯) |
33 | 31, 32, 13 | co 5874 |
. . . . . . . 8
class ((πβπ§) β (πβπ₯)) |
34 | 30, 22, 13 | co 5874 |
. . . . . . . 8
class (π§ β π₯) |
35 | | cdiv 8628 |
. . . . . . . 8
class
/ |
36 | 33, 34, 35 | co 5874 |
. . . . . . 7
class (((πβπ§) β (πβπ₯)) / (π§ β π₯)) |
37 | 24, 29, 36 | cmpt 4064 |
. . . . . 6
class (π§ β {π€ β dom π β£ π€ # π₯} β¦ (((πβπ§) β (πβπ₯)) / (π§ β π₯))) |
38 | | climc 14059 |
. . . . . 6
class
limβ |
39 | 37, 22, 38 | co 5874 |
. . . . 5
class ((π§ β {π€ β dom π β£ π€ # π₯} β¦ (((πβπ§) β (πβπ₯)) / (π§ β π₯))) limβ π₯) |
40 | 23, 39 | cxp 4624 |
. . . 4
class ({π₯} Γ ((π§ β {π€ β dom π β£ π€ # π₯} β¦ (((πβπ§) β (πβπ₯)) / (π§ β π₯))) limβ π₯)) |
41 | 9, 21, 40 | ciun 3886 |
. . 3
class βͺ π₯ β ((intβ((MetOpenβ(abs
β β )) βΎt π ))βdom π)({π₯} Γ ((π§ β {π€ β dom π β£ π€ # π₯} β¦ (((πβπ§) β (πβπ₯)) / (π§ β π₯))) limβ π₯)) |
42 | 2, 3, 5, 8, 41 | cmpo 5876 |
. 2
class (π β π« β, π β (β
βpm π ) β¦ βͺ
π₯ β
((intβ((MetOpenβ(abs β β )) βΎt π ))βdom π)({π₯} Γ ((π§ β {π€ β dom π β£ π€ # π₯} β¦ (((πβπ§) β (πβπ₯)) / (π§ β π₯))) limβ π₯))) |
43 | 1, 42 | wceq 1353 |
1
wff D = (π β π« β, π β (β
βpm π ) β¦ βͺ
π₯ β
((intβ((MetOpenβ(abs β β )) βΎt π ))βdom π)({π₯} Γ ((π§ β {π€ β dom π β£ π€ # π₯} β¦ (((πβπ§) β (πβπ₯)) / (π§ β π₯))) limβ π₯))) |