Step |
Hyp |
Ref |
Expression |
0 |
|
cinito |
|- InitO |
1 |
|
vc |
|- c |
2 |
|
ccat |
|- Cat |
3 |
|
va |
|- a |
4 |
|
cbs |
|- Base |
5 |
1
|
cv |
|- c |
6 |
5 4
|
cfv |
|- ( Base ` c ) |
7 |
|
vb |
|- b |
8 |
|
vh |
|- h |
9 |
8
|
cv |
|- h |
10 |
3
|
cv |
|- a |
11 |
|
chom |
|- Hom |
12 |
5 11
|
cfv |
|- ( Hom ` c ) |
13 |
7
|
cv |
|- b |
14 |
10 13 12
|
co |
|- ( a ( Hom ` c ) b ) |
15 |
9 14
|
wcel |
|- h e. ( a ( Hom ` c ) b ) |
16 |
15 8
|
weu |
|- E! h h e. ( a ( Hom ` c ) b ) |
17 |
16 7 6
|
wral |
|- A. b e. ( Base ` c ) E! h h e. ( a ( Hom ` c ) b ) |
18 |
17 3 6
|
crab |
|- { a e. ( Base ` c ) | A. b e. ( Base ` c ) E! h h e. ( a ( Hom ` c ) b ) } |
19 |
1 2 18
|
cmpt |
|- ( c e. Cat |-> { a e. ( Base ` c ) | A. b e. ( Base ` c ) E! h h e. ( a ( Hom ` c ) b ) } ) |
20 |
0 19
|
wceq |
|- InitO = ( c e. Cat |-> { a e. ( Base ` c ) | A. b e. ( Base ` c ) E! h h e. ( a ( Hom ` c ) b ) } ) |