Description: The ring of scalars of the dual of a vector space. (Contributed by NM, 18-Oct-2014)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ldualsca.f | |
|
ldualsca.o | |
||
ldualsca.d | |
||
ldualsca.r | |
||
ldualsca.w | |
||
Assertion | ldualsca | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ldualsca.f | |
|
2 | ldualsca.o | |
|
3 | ldualsca.d | |
|
4 | ldualsca.r | |
|
5 | ldualsca.w | |
|
6 | eqid | |
|
7 | eqid | |
|
8 | eqid | |
|
9 | eqid | |
|
10 | eqid | |
|
11 | eqid | |
|
12 | eqid | |
|
13 | 6 7 8 9 3 1 10 11 2 12 5 | ldualset | |
14 | 13 | fveq2d | |
15 | 2 | fvexi | |
16 | eqid | |
|
17 | 16 | lmodsca | |
18 | 15 17 | ax-mp | |
19 | 14 4 18 | 3eqtr4g | |