Step | Hyp | Ref
| Expression |
1 | | cend 36280 |
. 2
class
End |
2 | | vc |
. . 3
setvar π |
3 | | ccat 17610 |
. . 3
class
Cat |
4 | | vx |
. . . 4
setvar π₯ |
5 | 2 | cv 1540 |
. . . . 5
class π |
6 | | cbs 17146 |
. . . . 5
class
Base |
7 | 5, 6 | cfv 6543 |
. . . 4
class
(Baseβπ) |
8 | | cnx 17128 |
. . . . . . 7
class
ndx |
9 | 8, 6 | cfv 6543 |
. . . . . 6
class
(Baseβndx) |
10 | 4 | cv 1540 |
. . . . . . 7
class π₯ |
11 | | chom 17210 |
. . . . . . . 8
class
Hom |
12 | 5, 11 | cfv 6543 |
. . . . . . 7
class (Hom
βπ) |
13 | 10, 10, 12 | co 7411 |
. . . . . 6
class (π₯(Hom βπ)π₯) |
14 | 9, 13 | cop 4634 |
. . . . 5
class
β¨(Baseβndx), (π₯(Hom βπ)π₯)β© |
15 | | cplusg 17199 |
. . . . . . 7
class
+g |
16 | 8, 15 | cfv 6543 |
. . . . . 6
class
(+gβndx) |
17 | 10, 10 | cop 4634 |
. . . . . . 7
class
β¨π₯, π₯β© |
18 | | cco 17211 |
. . . . . . . 8
class
comp |
19 | 5, 18 | cfv 6543 |
. . . . . . 7
class
(compβπ) |
20 | 17, 10, 19 | co 7411 |
. . . . . 6
class
(β¨π₯, π₯β©(compβπ)π₯) |
21 | 16, 20 | cop 4634 |
. . . . 5
class
β¨(+gβndx), (β¨π₯, π₯β©(compβπ)π₯)β© |
22 | 14, 21 | cpr 4630 |
. . . 4
class
{β¨(Baseβndx), (π₯(Hom βπ)π₯)β©, β¨(+gβndx),
(β¨π₯, π₯β©(compβπ)π₯)β©} |
23 | 4, 7, 22 | cmpt 5231 |
. . 3
class (π₯ β (Baseβπ) β¦
{β¨(Baseβndx), (π₯(Hom βπ)π₯)β©, β¨(+gβndx),
(β¨π₯, π₯β©(compβπ)π₯)β©}) |
24 | 2, 3, 23 | cmpt 5231 |
. 2
class (π β Cat β¦ (π₯ β (Baseβπ) β¦
{β¨(Baseβndx), (π₯(Hom βπ)π₯)β©, β¨(+gβndx),
(β¨π₯, π₯β©(compβπ)π₯)β©})) |
25 | 1, 24 | wceq 1541 |
1
wff End =
(π β Cat β¦
(π₯ β (Baseβπ) β¦
{β¨(Baseβndx), (π₯(Hom βπ)π₯)β©, β¨(+gβndx),
(β¨π₯, π₯β©(compβπ)π₯)β©})) |