Description: Value of the set of ring ideals. (Contributed by Stefan O'Rear, 31-Mar-2015)
Ref | Expression | ||
---|---|---|---|
Assertion | lidlval | |- ( LIdeal ` W ) = ( LSubSp ` ( ringLMod ` W ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-lidl | |- LIdeal = ( LSubSp o. ringLMod ) |
|
2 | 1 | fveq1i | |- ( LIdeal ` W ) = ( ( LSubSp o. ringLMod ) ` W ) |
3 | 00lss | |- (/) = ( LSubSp ` (/) ) |
|
4 | rlmfn | |- ringLMod Fn _V |
|
5 | fnfun | |- ( ringLMod Fn _V -> Fun ringLMod ) |
|
6 | 4 5 | ax-mp | |- Fun ringLMod |
7 | 3 6 | fvco4i | |- ( ( LSubSp o. ringLMod ) ` W ) = ( LSubSp ` ( ringLMod ` W ) ) |
8 | 2 7 | eqtri | |- ( LIdeal ` W ) = ( LSubSp ` ( ringLMod ` W ) ) |