Step |
Hyp |
Ref |
Expression |
1 |
|
ringsubdi.b |
|
2 |
|
ringsubdi.t |
|
3 |
|
ringsubdi.m |
|
4 |
|
ringsubdi.r |
|
5 |
|
ringsubdi.x |
|
6 |
|
ringsubdi.y |
|
7 |
|
ringsubdi.z |
|
8 |
|
ringgrp |
|
9 |
4 8
|
syl |
|
10 |
|
eqid |
|
11 |
1 10
|
grpinvcl |
|
12 |
9 6 11
|
syl2anc |
|
13 |
|
eqid |
|
14 |
1 13 2
|
ringdir |
|
15 |
4 5 12 7 14
|
syl13anc |
|
16 |
1 2 10 4 6 7
|
ringmneg1 |
|
17 |
16
|
oveq2d |
|
18 |
15 17
|
eqtrd |
|
19 |
1 13 10 3
|
grpsubval |
|
20 |
5 6 19
|
syl2anc |
|
21 |
20
|
oveq1d |
|
22 |
1 2
|
ringcl |
|
23 |
4 5 7 22
|
syl3anc |
|
24 |
1 2
|
ringcl |
|
25 |
4 6 7 24
|
syl3anc |
|
26 |
1 13 10 3
|
grpsubval |
|
27 |
23 25 26
|
syl2anc |
|
28 |
18 21 27
|
3eqtr4d |
|