Description: Obsolete version of zlmbas as of 3-Nov-2024. Ring operation of a ZZ -module (if present). (Contributed by Mario Carneiro, 2-Oct-2015) (New usage is discouraged.) (Proof modification is discouraged.)
| Ref | Expression | ||
|---|---|---|---|
| Hypotheses | zlmbas.w | |- W = ( ZMod ` G ) |
|
| zlmmulr.2 | |- .x. = ( .r ` G ) |
||
| Assertion | zlmmulrOLD | |- .x. = ( .r ` W ) |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | zlmbas.w | |- W = ( ZMod ` G ) |
|
| 2 | zlmmulr.2 | |- .x. = ( .r ` G ) |
|
| 3 | df-mulr | |- .r = Slot 3 |
|
| 4 | 3nn | |- 3 e. NN |
|
| 5 | 3lt5 | |- 3 < 5 |
|
| 6 | 1 3 4 5 | zlmlemOLD | |- ( .r ` G ) = ( .r ` W ) |
| 7 | 2 6 | eqtri | |- .x. = ( .r ` W ) |