Description: The scalar component of a left module is an additive group. (Contributed by NM, 8-Dec-2013) (Revised by Mario Carneiro, 19-Jun-2014)
| Ref | Expression | ||
|---|---|---|---|
| Hypothesis | lmodring.1 | |- F = ( Scalar ` W ) |
|
| Assertion | lmodfgrp | |- ( W e. LMod -> F e. Grp ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | lmodring.1 | |- F = ( Scalar ` W ) |
|
| 2 | 1 | lmodring | |- ( W e. LMod -> F e. Ring ) |
| 3 | ringgrp | |- ( F e. Ring -> F e. Grp ) |
|
| 4 | 2 3 | syl | |- ( W e. LMod -> F e. Grp ) |