Step |
Hyp |
Ref |
Expression |
1 |
|
tngnrg.t |
|
2 |
|
tngnrg.a |
|
3 |
2
|
abvrcl |
|
4 |
|
ringgrp |
|
5 |
3 4
|
syl |
|
6 |
|
eqid |
|
7 |
1 6
|
tngds |
|
8 |
|
eqid |
|
9 |
8 2 6
|
abvmet |
|
10 |
7 9
|
eqeltrrd |
|
11 |
2 8
|
abvf |
|
12 |
|
eqid |
|
13 |
1 8 12
|
tngngp2 |
|
14 |
11 13
|
syl |
|
15 |
5 10 14
|
mpbir2and |
|
16 |
|
reex |
|
17 |
1 8 16
|
tngnm |
|
18 |
5 11 17
|
syl2anc |
|
19 |
|
eqidd |
|
20 |
1 8
|
tngbas |
|
21 |
|
eqid |
|
22 |
1 21
|
tngplusg |
|
23 |
22
|
oveqdr |
|
24 |
|
eqid |
|
25 |
1 24
|
tngmulr |
|
26 |
25
|
oveqdr |
|
27 |
19 20 23 26
|
abvpropd |
|
28 |
2 27
|
syl5eq |
|
29 |
18 28
|
eleq12d |
|
30 |
29
|
ibi |
|
31 |
|
eqid |
|
32 |
|
eqid |
|
33 |
31 32
|
isnrg |
|
34 |
15 30 33
|
sylanbrc |
|