Step |
Hyp |
Ref |
Expression |
1 |
|
ply1val.1 |
|- P = ( Poly1 ` R ) |
2 |
|
ply1bas.u |
|- U = ( Base ` P ) |
3 |
|
eqid |
|- ( 1o mPoly R ) = ( 1o mPoly R ) |
4 |
|
eqid |
|- ( 1o mPwSer R ) = ( 1o mPwSer R ) |
5 |
|
eqid |
|- ( Base ` ( 1o mPoly R ) ) = ( Base ` ( 1o mPoly R ) ) |
6 |
|
eqid |
|- ( PwSer1 ` R ) = ( PwSer1 ` R ) |
7 |
|
eqid |
|- ( Base ` ( PwSer1 ` R ) ) = ( Base ` ( PwSer1 ` R ) ) |
8 |
6 7 4
|
psr1bas2 |
|- ( Base ` ( PwSer1 ` R ) ) = ( Base ` ( 1o mPwSer R ) ) |
9 |
3 4 5 8
|
mplbasss |
|- ( Base ` ( 1o mPoly R ) ) C_ ( Base ` ( PwSer1 ` R ) ) |
10 |
1 6
|
ply1val |
|- P = ( ( PwSer1 ` R ) |`s ( Base ` ( 1o mPoly R ) ) ) |
11 |
10 7
|
ressbas2 |
|- ( ( Base ` ( 1o mPoly R ) ) C_ ( Base ` ( PwSer1 ` R ) ) -> ( Base ` ( 1o mPoly R ) ) = ( Base ` P ) ) |
12 |
9 11
|
ax-mp |
|- ( Base ` ( 1o mPoly R ) ) = ( Base ` P ) |
13 |
2 12
|
eqtr4i |
|- U = ( Base ` ( 1o mPoly R ) ) |