Step |
Hyp |
Ref |
Expression |
1 |
|
dchrmhm.g |
|- G = ( DChr ` N ) |
2 |
|
dchrmhm.z |
|- Z = ( Z/nZ ` N ) |
3 |
|
dchrmhm.b |
|- D = ( Base ` G ) |
4 |
|
eqid |
|- ( Base ` Z ) = ( Base ` Z ) |
5 |
|
eqid |
|- ( Unit ` Z ) = ( Unit ` Z ) |
6 |
1 3
|
dchrrcl |
|- ( x e. D -> N e. NN ) |
7 |
1 2 4 5 6 3
|
dchrelbas |
|- ( x e. D -> ( x e. D <-> ( x e. ( ( mulGrp ` Z ) MndHom ( mulGrp ` CCfld ) ) /\ ( ( ( Base ` Z ) \ ( Unit ` Z ) ) X. { 0 } ) C_ x ) ) ) |
8 |
7
|
ibi |
|- ( x e. D -> ( x e. ( ( mulGrp ` Z ) MndHom ( mulGrp ` CCfld ) ) /\ ( ( ( Base ` Z ) \ ( Unit ` Z ) ) X. { 0 } ) C_ x ) ) |
9 |
8
|
simpld |
|- ( x e. D -> x e. ( ( mulGrp ` Z ) MndHom ( mulGrp ` CCfld ) ) ) |
10 |
9
|
ssriv |
|- D C_ ( ( mulGrp ` Z ) MndHom ( mulGrp ` CCfld ) ) |