Step |
Hyp |
Ref |
Expression |
1 |
|
matassa.a |
|
2 |
|
eqid |
|
3 |
1 2
|
matbas2 |
|
4 |
1
|
matsca2 |
|
5 |
|
eqidd |
|
6 |
|
eqidd |
|
7 |
|
eqid |
|
8 |
1 7
|
matmulr |
|
9 |
|
crngring |
|
10 |
1
|
matlmod |
|
11 |
9 10
|
sylan2 |
|
12 |
1
|
matring |
|
13 |
9 12
|
sylan2 |
|
14 |
9
|
ad2antlr |
|
15 |
|
simpll |
|
16 |
|
eqid |
|
17 |
|
simpr1 |
|
18 |
|
simpr2 |
|
19 |
|
simpr3 |
|
20 |
2 14 7 15 15 15 16 17 18 19
|
mamuvs1 |
|
21 |
3
|
adantr |
|
22 |
18 21
|
eleqtrd |
|
23 |
|
eqid |
|
24 |
|
eqid |
|
25 |
|
eqid |
|
26 |
1 23 2 24 16 25
|
matvsca2 |
|
27 |
17 22 26
|
syl2anc |
|
28 |
27
|
oveq1d |
|
29 |
2 14 7 15 15 15 18 19
|
mamucl |
|
30 |
29 21
|
eleqtrd |
|
31 |
1 23 2 24 16 25
|
matvsca2 |
|
32 |
17 30 31
|
syl2anc |
|
33 |
20 28 32
|
3eqtr4d |
|
34 |
|
simplr |
|
35 |
34 2 16 7 15 15 15 18 17 19
|
mamuvs2 |
|
36 |
19 21
|
eleqtrd |
|
37 |
1 23 2 24 16 25
|
matvsca2 |
|
38 |
17 36 37
|
syl2anc |
|
39 |
38
|
oveq2d |
|
40 |
35 39 32
|
3eqtr4d |
|
41 |
3 4 5 6 8 11 13 33 40
|
isassad |
|