Step |
Hyp |
Ref |
Expression |
1 |
|
nminvr.n |
|
2 |
|
nminvr.u |
|
3 |
|
nminvr.i |
|
4 |
|
nrgngp |
|
5 |
4
|
3ad2ant1 |
|
6 |
|
eqid |
|
7 |
6 2
|
unitcl |
|
8 |
7
|
3ad2ant3 |
|
9 |
6 1
|
nmcl |
|
10 |
5 8 9
|
syl2anc |
|
11 |
10
|
recnd |
|
12 |
|
nzrring |
|
13 |
12
|
3ad2ant2 |
|
14 |
|
simp3 |
|
15 |
2 3 6
|
ringinvcl |
|
16 |
13 14 15
|
syl2anc |
|
17 |
6 1
|
nmcl |
|
18 |
5 16 17
|
syl2anc |
|
19 |
18
|
recnd |
|
20 |
1 2
|
unitnmn0 |
|
21 |
|
eqid |
|
22 |
|
eqid |
|
23 |
2 3 21 22
|
unitrinv |
|
24 |
13 14 23
|
syl2anc |
|
25 |
24
|
fveq2d |
|
26 |
|
simp1 |
|
27 |
6 1 21
|
nmmul |
|
28 |
26 8 16 27
|
syl3anc |
|
29 |
1 22
|
nm1 |
|
30 |
29
|
3adant3 |
|
31 |
25 28 30
|
3eqtr3d |
|
32 |
11 19 20 31
|
mvllmuld |
|