Step |
Hyp |
Ref |
Expression |
0 |
|
cidfu |
|- idFunc |
1 |
|
vt |
|- t |
2 |
|
ccat |
|- Cat |
3 |
|
cbs |
|- Base |
4 |
1
|
cv |
|- t |
5 |
4 3
|
cfv |
|- ( Base ` t ) |
6 |
|
vb |
|- b |
7 |
|
cid |
|- _I |
8 |
6
|
cv |
|- b |
9 |
7 8
|
cres |
|- ( _I |` b ) |
10 |
|
vz |
|- z |
11 |
8 8
|
cxp |
|- ( b X. b ) |
12 |
|
chom |
|- Hom |
13 |
4 12
|
cfv |
|- ( Hom ` t ) |
14 |
10
|
cv |
|- z |
15 |
14 13
|
cfv |
|- ( ( Hom ` t ) ` z ) |
16 |
7 15
|
cres |
|- ( _I |` ( ( Hom ` t ) ` z ) ) |
17 |
10 11 16
|
cmpt |
|- ( z e. ( b X. b ) |-> ( _I |` ( ( Hom ` t ) ` z ) ) ) |
18 |
9 17
|
cop |
|- <. ( _I |` b ) , ( z e. ( b X. b ) |-> ( _I |` ( ( Hom ` t ) ` z ) ) ) >. |
19 |
6 5 18
|
csb |
|- [_ ( Base ` t ) / b ]_ <. ( _I |` b ) , ( z e. ( b X. b ) |-> ( _I |` ( ( Hom ` t ) ` z ) ) ) >. |
20 |
1 2 19
|
cmpt |
|- ( t e. Cat |-> [_ ( Base ` t ) / b ]_ <. ( _I |` b ) , ( z e. ( b X. b ) |-> ( _I |` ( ( Hom ` t ) ` z ) ) ) >. ) |
21 |
0 20
|
wceq |
|- idFunc = ( t e. Cat |-> [_ ( Base ` t ) / b ]_ <. ( _I |` b ) , ( z e. ( b X. b ) |-> ( _I |` ( ( Hom ` t ) ` z ) ) ) >. ) |