Step |
Hyp |
Ref |
Expression |
1 |
|
dvrcan5.b |
|
2 |
|
dvrcan5.o |
|
3 |
|
dvrcan5.d |
|
4 |
|
dvrcan5.t |
|
5 |
1 2
|
unitss |
|
6 |
|
simpr3 |
|
7 |
5 6
|
sselid |
|
8 |
2 4
|
unitmulcl |
|
9 |
8
|
3adant3r1 |
|
10 |
|
eqid |
|
11 |
1 4 2 10 3
|
dvrval |
|
12 |
7 9 11
|
syl2anc |
|
13 |
|
simpl |
|
14 |
|
eqid |
|
15 |
2 14
|
unitgrp |
|
16 |
13 15
|
syl |
|
17 |
|
simpr2 |
|
18 |
2 14
|
unitgrpbas |
|
19 |
2
|
fvexi |
|
20 |
|
eqid |
|
21 |
20 4
|
mgpplusg |
|
22 |
14 21
|
ressplusg |
|
23 |
19 22
|
ax-mp |
|
24 |
2 14 10
|
invrfval |
|
25 |
18 23 24
|
grpinvadd |
|
26 |
25
|
oveq2d |
|
27 |
16 17 6 26
|
syl3anc |
|
28 |
|
eqid |
|
29 |
2 10 4 28
|
unitrinv |
|
30 |
29
|
oveq1d |
|
31 |
30
|
3ad2antr3 |
|
32 |
2 10
|
unitinvcl |
|
33 |
32
|
3ad2antr3 |
|
34 |
5 33
|
sselid |
|
35 |
2 10
|
unitinvcl |
|
36 |
35
|
3ad2antr2 |
|
37 |
5 36
|
sselid |
|
38 |
1 4
|
ringass |
|
39 |
13 7 34 37 38
|
syl13anc |
|
40 |
1 4 28
|
ringlidm |
|
41 |
13 37 40
|
syl2anc |
|
42 |
31 39 41
|
3eqtr3d |
|
43 |
12 27 42
|
3eqtrd |
|
44 |
43
|
oveq2d |
|
45 |
|
simpr1 |
|
46 |
1 2 3 4
|
dvrass |
|
47 |
13 45 7 9 46
|
syl13anc |
|
48 |
1 4 2 10 3
|
dvrval |
|
49 |
45 17 48
|
syl2anc |
|
50 |
44 47 49
|
3eqtr4d |
|