Step |
Hyp |
Ref |
Expression |
1 |
|
ply1baspropd.b1 |
|- ( ph -> B = ( Base ` R ) ) |
2 |
|
ply1baspropd.b2 |
|- ( ph -> B = ( Base ` S ) ) |
3 |
|
ply1baspropd.p |
|- ( ( ph /\ ( x e. B /\ y e. B ) ) -> ( x ( +g ` R ) y ) = ( x ( +g ` S ) y ) ) |
4 |
1 2 3
|
mplbaspropd |
|- ( ph -> ( Base ` ( 1o mPoly R ) ) = ( Base ` ( 1o mPoly S ) ) ) |
5 |
|
eqid |
|- ( Poly1 ` R ) = ( Poly1 ` R ) |
6 |
|
eqid |
|- ( Base ` ( Poly1 ` R ) ) = ( Base ` ( Poly1 ` R ) ) |
7 |
5 6
|
ply1bas |
|- ( Base ` ( Poly1 ` R ) ) = ( Base ` ( 1o mPoly R ) ) |
8 |
|
eqid |
|- ( Poly1 ` S ) = ( Poly1 ` S ) |
9 |
|
eqid |
|- ( Base ` ( Poly1 ` S ) ) = ( Base ` ( Poly1 ` S ) ) |
10 |
8 9
|
ply1bas |
|- ( Base ` ( Poly1 ` S ) ) = ( Base ` ( 1o mPoly S ) ) |
11 |
4 7 10
|
3eqtr4g |
|- ( ph -> ( Base ` ( Poly1 ` R ) ) = ( Base ` ( Poly1 ` S ) ) ) |