Step |
Hyp |
Ref |
Expression |
1 |
|
kerunit.1 |
|
2 |
|
kerunit.2 |
|
3 |
|
kerunit.3 |
|
4 |
|
elin |
|
5 |
4
|
biimpi |
|
6 |
5
|
adantl |
|
7 |
6
|
simpld |
|
8 |
|
rhmrcl1 |
|
9 |
|
eqid |
|
10 |
|
eqid |
|
11 |
|
eqid |
|
12 |
1 9 10 11
|
unitlinv |
|
13 |
12
|
fveq2d |
|
14 |
8 13
|
sylan |
|
15 |
7 14
|
syldan |
|
16 |
|
simpl |
|
17 |
8
|
adantr |
|
18 |
|
eqid |
|
19 |
1 9 18
|
ringinvcl |
|
20 |
17 7 19
|
syl2anc |
|
21 |
18 1
|
unitcl |
|
22 |
7 21
|
syl |
|
23 |
|
eqid |
|
24 |
18 10 23
|
rhmmul |
|
25 |
16 20 22 24
|
syl3anc |
|
26 |
6
|
simprd |
|
27 |
|
eqid |
|
28 |
18 27
|
rhmf |
|
29 |
|
ffn |
|
30 |
|
elpreima |
|
31 |
28 29 30
|
3syl |
|
32 |
31
|
simplbda |
|
33 |
26 32
|
syldan |
|
34 |
|
fvex |
|
35 |
34
|
elsn |
|
36 |
33 35
|
sylib |
|
37 |
36
|
oveq2d |
|
38 |
|
rhmrcl2 |
|
39 |
38
|
adantr |
|
40 |
28
|
adantr |
|
41 |
40 20
|
ffvelrnd |
|
42 |
27 23 2
|
ringrz |
|
43 |
39 41 42
|
syl2anc |
|
44 |
25 37 43
|
3eqtrd |
|
45 |
11 3
|
rhm1 |
|
46 |
45
|
adantr |
|
47 |
15 44 46
|
3eqtr3rd |
|
48 |
47
|
reximdva0 |
|
49 |
|
id |
|
50 |
49
|
rexlimivw |
|
51 |
48 50
|
syl |
|