Description: The ring module over a division ring is a vector space. (Contributed by Mario Carneiro, 4-Oct-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | rlmlvec | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | drngring | |
|
2 | rlmlmod | |
|
3 | 1 2 | syl | |
4 | rlmsca | |
|
5 | id | |
|
6 | 4 5 | eqeltrrd | |
7 | eqid | |
|
8 | 7 | islvec | |
9 | 3 6 8 | sylanbrc | |