Step |
Hyp |
Ref |
Expression |
1 |
|
nmmul.x |
|
2 |
|
nmmul.n |
|
3 |
|
nmmul.t |
|
4 |
|
nrgdsdi.d |
|
5 |
|
simpl |
|
6 |
|
nrgring |
|
7 |
6
|
adantr |
|
8 |
|
ringgrp |
|
9 |
7 8
|
syl |
|
10 |
|
simpr1 |
|
11 |
|
simpr2 |
|
12 |
|
eqid |
|
13 |
1 12
|
grpsubcl |
|
14 |
9 10 11 13
|
syl3anc |
|
15 |
|
simpr3 |
|
16 |
1 2 3
|
nmmul |
|
17 |
5 14 15 16
|
syl3anc |
|
18 |
1 3 12 7 10 11 15
|
rngsubdir |
|
19 |
18
|
fveq2d |
|
20 |
17 19
|
eqtr3d |
|
21 |
|
nrgngp |
|
22 |
21
|
adantr |
|
23 |
2 1 12 4
|
ngpds |
|
24 |
22 10 11 23
|
syl3anc |
|
25 |
24
|
oveq1d |
|
26 |
1 3
|
ringcl |
|
27 |
7 10 15 26
|
syl3anc |
|
28 |
1 3
|
ringcl |
|
29 |
7 11 15 28
|
syl3anc |
|
30 |
2 1 12 4
|
ngpds |
|
31 |
22 27 29 30
|
syl3anc |
|
32 |
20 25 31
|
3eqtr4d |
|