Step |
Hyp |
Ref |
Expression |
1 |
|
idomsubgmo.g |
|
2 |
|
proot1mul.o |
|
3 |
|
proot1mul.k |
|
4 |
|
simpll |
|
5 |
|
isidom |
|
6 |
5
|
simprbi |
|
7 |
|
domnring |
|
8 |
|
eqid |
|
9 |
8 1
|
unitgrp |
|
10 |
4 6 7 9
|
4syl |
|
11 |
|
eqid |
|
12 |
11
|
subgacs |
|
13 |
|
acsmre |
|
14 |
10 12 13
|
3syl |
|
15 |
|
simprl |
|
16 |
11 2
|
odf |
|
17 |
|
ffn |
|
18 |
|
fniniseg |
|
19 |
16 17 18
|
mp2b |
|
20 |
15 19
|
sylib |
|
21 |
20
|
simpld |
|
22 |
21
|
snssd |
|
23 |
14 3 22
|
mrcssidd |
|
24 |
|
snssg |
|
25 |
15 24
|
syl |
|
26 |
23 25
|
mpbird |
|
27 |
1
|
idomsubgmo |
|
28 |
27
|
adantr |
|
29 |
3
|
mrccl |
|
30 |
14 22 29
|
syl2anc |
|
31 |
20
|
simprd |
|
32 |
|
simplr |
|
33 |
31 32
|
eqeltrd |
|
34 |
11 2 3
|
odhash2 |
|
35 |
10 21 33 34
|
syl3anc |
|
36 |
35 31
|
eqtrd |
|
37 |
|
simprr |
|
38 |
|
fniniseg |
|
39 |
16 17 38
|
mp2b |
|
40 |
37 39
|
sylib |
|
41 |
40
|
simpld |
|
42 |
41
|
snssd |
|
43 |
3
|
mrccl |
|
44 |
14 42 43
|
syl2anc |
|
45 |
40
|
simprd |
|
46 |
45 32
|
eqeltrd |
|
47 |
11 2 3
|
odhash2 |
|
48 |
10 41 46 47
|
syl3anc |
|
49 |
48 45
|
eqtrd |
|
50 |
|
fveqeq2 |
|
51 |
|
fveqeq2 |
|
52 |
50 51
|
rmoi |
|
53 |
28 30 36 44 49 52
|
syl122anc |
|
54 |
26 53
|
eleqtrd |
|