Step |
Hyp |
Ref |
Expression |
1 |
|
efmndbas.g |
|- G = ( EndoFMnd ` A ) |
2 |
|
efmndbas.b |
|- B = ( Base ` G ) |
3 |
1 2
|
efmndbas |
|- B = ( A ^m A ) |
4 |
|
mapvalg |
|- ( ( A e. _V /\ A e. _V ) -> ( A ^m A ) = { f | f : A --> A } ) |
5 |
4
|
anidms |
|- ( A e. _V -> ( A ^m A ) = { f | f : A --> A } ) |
6 |
3 5
|
eqtrid |
|- ( A e. _V -> B = { f | f : A --> A } ) |
7 |
|
base0 |
|- (/) = ( Base ` (/) ) |
8 |
7
|
eqcomi |
|- ( Base ` (/) ) = (/) |
9 |
|
fvprc |
|- ( -. A e. _V -> ( EndoFMnd ` A ) = (/) ) |
10 |
1 9
|
eqtrid |
|- ( -. A e. _V -> G = (/) ) |
11 |
10
|
fveq2d |
|- ( -. A e. _V -> ( Base ` G ) = ( Base ` (/) ) ) |
12 |
2 11
|
eqtrid |
|- ( -. A e. _V -> B = ( Base ` (/) ) ) |
13 |
|
mapprc |
|- ( -. A e. _V -> { f | f : A --> A } = (/) ) |
14 |
8 12 13
|
3eqtr4a |
|- ( -. A e. _V -> B = { f | f : A --> A } ) |
15 |
6 14
|
pm2.61i |
|- B = { f | f : A --> A } |