Step | Hyp | Ref
| Expression |
1 | | ccnext 23433 |
. 2
class
CnExt |
2 | | vj |
. . 3
setvar π |
3 | | vk |
. . 3
setvar π |
4 | | ctop 22265 |
. . 3
class
Top |
5 | | vf |
. . . 4
setvar π |
6 | 3 | cv 1541 |
. . . . . 6
class π |
7 | 6 | cuni 4869 |
. . . . 5
class βͺ π |
8 | 2 | cv 1541 |
. . . . . 6
class π |
9 | 8 | cuni 4869 |
. . . . 5
class βͺ π |
10 | | cpm 8772 |
. . . . 5
class
βpm |
11 | 7, 9, 10 | co 7361 |
. . . 4
class (βͺ π
βpm βͺ π) |
12 | | vx |
. . . . 5
setvar π₯ |
13 | 5 | cv 1541 |
. . . . . . 7
class π |
14 | 13 | cdm 5637 |
. . . . . 6
class dom π |
15 | | ccl 22392 |
. . . . . . 7
class
cls |
16 | 8, 15 | cfv 6500 |
. . . . . 6
class
(clsβπ) |
17 | 14, 16 | cfv 6500 |
. . . . 5
class
((clsβπ)βdom π) |
18 | 12 | cv 1541 |
. . . . . . 7
class π₯ |
19 | 18 | csn 4590 |
. . . . . 6
class {π₯} |
20 | | cnei 22471 |
. . . . . . . . . . 11
class
nei |
21 | 8, 20 | cfv 6500 |
. . . . . . . . . 10
class
(neiβπ) |
22 | 19, 21 | cfv 6500 |
. . . . . . . . 9
class
((neiβπ)β{π₯}) |
23 | | crest 17310 |
. . . . . . . . 9
class
βΎt |
24 | 22, 14, 23 | co 7361 |
. . . . . . . 8
class
(((neiβπ)β{π₯}) βΎt dom π) |
25 | | cflf 23309 |
. . . . . . . 8
class
fLimf |
26 | 6, 24, 25 | co 7361 |
. . . . . . 7
class (π fLimf (((neiβπ)β{π₯}) βΎt dom π)) |
27 | 13, 26 | cfv 6500 |
. . . . . 6
class ((π fLimf (((neiβπ)β{π₯}) βΎt dom π))βπ) |
28 | 19, 27 | cxp 5635 |
. . . . 5
class ({π₯} Γ ((π fLimf (((neiβπ)β{π₯}) βΎt dom π))βπ)) |
29 | 12, 17, 28 | ciun 4958 |
. . . 4
class βͺ π₯ β ((clsβπ)βdom π)({π₯} Γ ((π fLimf (((neiβπ)β{π₯}) βΎt dom π))βπ)) |
30 | 5, 11, 29 | cmpt 5192 |
. . 3
class (π β (βͺ π
βpm βͺ π) β¦ βͺ
π₯ β ((clsβπ)βdom π)({π₯} Γ ((π fLimf (((neiβπ)β{π₯}) βΎt dom π))βπ))) |
31 | 2, 3, 4, 4, 30 | cmpo 7363 |
. 2
class (π β Top, π β Top β¦ (π β (βͺ π βpm βͺ π)
β¦ βͺ π₯ β ((clsβπ)βdom π)({π₯} Γ ((π fLimf (((neiβπ)β{π₯}) βΎt dom π))βπ)))) |
32 | 1, 31 | wceq 1542 |
1
wff CnExt =
(π β Top, π β Top β¦ (π β (βͺ π
βpm βͺ π) β¦ βͺ
π₯ β ((clsβπ)βdom π)({π₯} Γ ((π fLimf (((neiβπ)β{π₯}) βΎt dom π))βπ)))) |