Metamath Proof Explorer


Theorem mplgrp

Description: The polynomial ring is a group. (Contributed by Mario Carneiro, 9-Jan-2015)

Ref Expression
Hypothesis mplgrp.p P = I mPoly R
Assertion mplgrp I V R Grp P Grp

Proof

Step Hyp Ref Expression
1 mplgrp.p P = I mPoly R
2 eqid I mPwSer R = I mPwSer R
3 eqid Base P = Base P
4 simpl I V R Grp I V
5 simpr I V R Grp R Grp
6 2 1 3 4 5 mplsubg I V R Grp Base P SubGrp I mPwSer R
7 1 2 3 mplval2 P = I mPwSer R 𝑠 Base P
8 7 subggrp Base P SubGrp I mPwSer R P Grp
9 6 8 syl I V R Grp P Grp