Description: Associative law for scalar product. Analogue of lmodvsass . (Contributed by Mario Carneiro, 16-Oct-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | clmvscl.v | |
|
clmvscl.f | |
||
clmvscl.s | |
||
clmvscl.k | |
||
Assertion | clmvsass | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | clmvscl.v | |
|
2 | clmvscl.f | |
|
3 | clmvscl.s | |
|
4 | clmvscl.k | |
|
5 | 2 | clmmul | |
6 | 5 | adantr | |
7 | 6 | oveqd | |
8 | 7 | oveq1d | |
9 | clmlmod | |
|
10 | eqid | |
|
11 | 1 2 3 4 10 | lmodvsass | |
12 | 9 11 | sylan | |
13 | 8 12 | eqtrd | |