Description: Replacing a row of a square matrix by a row with 0's and a 1 results in a square matrix of the same dimension. (Contributed by AV, 30-Dec-2018)
Ref | Expression | ||
---|---|---|---|
Hypotheses | marep01ma.a | |
|
marep01ma.b | |
||
marep01ma.r | |
||
marep01ma.0 | |
||
marep01ma.1 | |
||
Assertion | marep01ma | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | marep01ma.a | |
|
2 | marep01ma.b | |
|
3 | marep01ma.r | |
|
4 | marep01ma.0 | |
|
5 | marep01ma.1 | |
|
6 | eqid | |
|
7 | 1 2 | matrcl | |
8 | 7 | simpld | |
9 | 3 | a1i | |
10 | crngring | |
|
11 | 6 5 | ringidcl | |
12 | 3 10 11 | mp2b | |
13 | 6 4 | ring0cl | |
14 | 3 10 13 | mp2b | |
15 | 12 14 | ifcli | |
16 | 15 | a1i | |
17 | simp2 | |
|
18 | simp3 | |
|
19 | id | |
|
20 | 19 2 | eleqtrdi | |
21 | 20 | 3ad2ant1 | |
22 | 1 6 | matecl | |
23 | 17 18 21 22 | syl3anc | |
24 | 16 23 | ifcld | |
25 | 1 6 2 8 9 24 | matbas2d | |