Description: An entry of an N x N scalar matrix over the ring R . (Contributed by AV, 18-Dec-2019)
Ref | Expression | ||
---|---|---|---|
Hypotheses | scmatmat.a | |
|
scmatmat.b | |
||
scmatmat.s | |
||
scmate.k | |
||
scmate.0 | |
||
Assertion | scmate | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | scmatmat.a | |
|
2 | scmatmat.b | |
|
3 | scmatmat.s | |
|
4 | scmate.k | |
|
5 | scmate.0 | |
|
6 | eqid | |
|
7 | eqid | |
|
8 | 4 1 2 6 7 3 | scmatscmid | |
9 | oveq | |
|
10 | simpll1 | |
|
11 | simpll2 | |
|
12 | simpr | |
|
13 | simplr | |
|
14 | 1 4 5 6 7 | scmatscmide | |
15 | 10 11 12 13 14 | syl31anc | |
16 | 9 15 | sylan9eqr | |
17 | 16 | ex | |
18 | 17 | reximdva | |
19 | 18 | ex | |
20 | 8 19 | mpid | |
21 | 20 | imp | |