Description: The scalar product of the identity polynomial matrix with a polynomial is a polynomial matrix. (Contributed by AV, 2-Nov-2019) (Revised by AV, 4-Dec-2019)
Ref | Expression | ||
---|---|---|---|
Hypotheses | 1pmatscmul.p | |
|
1pmatscmul.c | |
||
1pmatscmul.b | |
||
1pmatscmul.e | |
||
1pmatscmul.m | |
||
1pmatscmul.1 | |
||
Assertion | 1pmatscmul | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 1pmatscmul.p | |
|
2 | 1pmatscmul.c | |
|
3 | 1pmatscmul.b | |
|
4 | 1pmatscmul.e | |
|
5 | 1pmatscmul.m | |
|
6 | 1pmatscmul.1 | |
|
7 | 1 | ply1ring | |
8 | 7 | anim2i | |
9 | 8 | 3adant3 | |
10 | simp3 | |
|
11 | 1 2 | pmatring | |
12 | 11 | 3adant3 | |
13 | 3 6 | ringidcl | |
14 | 12 13 | syl | |
15 | 4 2 3 5 | matvscl | |
16 | 9 10 14 15 | syl12anc | |