Step |
Hyp |
Ref |
Expression |
1 |
|
rhmrcl1 |
|
2 |
|
eqid |
|
3 |
|
eqid |
|
4 |
|
eqid |
|
5 |
|
eqid |
|
6 |
2 3 4 5
|
unitlinv |
|
7 |
1 6
|
sylan |
|
8 |
7
|
fveq2d |
|
9 |
|
simpl |
|
10 |
|
eqid |
|
11 |
10 2
|
unitss |
|
12 |
2 3
|
unitinvcl |
|
13 |
1 12
|
sylan |
|
14 |
11 13
|
sselid |
|
15 |
|
simpr |
|
16 |
11 15
|
sselid |
|
17 |
|
eqid |
|
18 |
10 4 17
|
rhmmul |
|
19 |
9 14 16 18
|
syl3anc |
|
20 |
|
eqid |
|
21 |
5 20
|
rhm1 |
|
22 |
21
|
adantr |
|
23 |
8 19 22
|
3eqtr3d |
|
24 |
|
rhmrcl2 |
|
25 |
24
|
adantr |
|
26 |
|
elrhmunit |
|
27 |
|
eqid |
|
28 |
|
eqid |
|
29 |
27 28 17 20
|
unitlinv |
|
30 |
25 26 29
|
syl2anc |
|
31 |
23 30
|
eqtr4d |
|
32 |
|
eqid |
|
33 |
27 32
|
unitgrp |
|
34 |
24 33
|
syl |
|
35 |
34
|
adantr |
|
36 |
|
elrhmunit |
|
37 |
13 36
|
syldan |
|
38 |
27 28
|
unitinvcl |
|
39 |
25 26 38
|
syl2anc |
|
40 |
27 32
|
unitgrpbas |
|
41 |
|
fvex |
|
42 |
|
eqid |
|
43 |
42 17
|
mgpplusg |
|
44 |
32 43
|
ressplusg |
|
45 |
41 44
|
ax-mp |
|
46 |
40 45
|
grprcan |
|
47 |
35 37 39 26 46
|
syl13anc |
|
48 |
31 47
|
mpbid |
|