Step |
Hyp |
Ref |
Expression |
1 |
|
ressply1.s |
|- S = ( Poly1 ` R ) |
2 |
|
ressply1.h |
|- H = ( R |`s T ) |
3 |
|
ressply1.u |
|- U = ( Poly1 ` H ) |
4 |
|
ressply1.b |
|- B = ( Base ` U ) |
5 |
|
ressply1.2 |
|- ( ph -> T e. ( SubRing ` R ) ) |
6 |
|
ressply1.p |
|- P = ( S |`s B ) |
7 |
|
eqid |
|- ( PwSer1 ` H ) = ( PwSer1 ` H ) |
8 |
|
eqid |
|- ( Base ` ( PwSer1 ` H ) ) = ( Base ` ( PwSer1 ` H ) ) |
9 |
|
eqid |
|- ( Base ` S ) = ( Base ` S ) |
10 |
1 2 3 4 5 7 8 9
|
ressply1bas2 |
|- ( ph -> B = ( ( Base ` ( PwSer1 ` H ) ) i^i ( Base ` S ) ) ) |
11 |
|
inss2 |
|- ( ( Base ` ( PwSer1 ` H ) ) i^i ( Base ` S ) ) C_ ( Base ` S ) |
12 |
10 11
|
eqsstrdi |
|- ( ph -> B C_ ( Base ` S ) ) |
13 |
6 9
|
ressbas2 |
|- ( B C_ ( Base ` S ) -> B = ( Base ` P ) ) |
14 |
12 13
|
syl |
|- ( ph -> B = ( Base ` P ) ) |