Step |
Hyp |
Ref |
Expression |
1 |
|
tnglvec.t |
|
2 |
|
eqidd |
|
3 |
|
eqid |
|
4 |
1 3
|
tngbas |
|
5 |
4
|
adantl |
|
6 |
|
ssidd |
|
7 |
|
eqid |
|
8 |
1 7
|
tngplusg |
|
9 |
8
|
adantl |
|
10 |
9
|
oveqdr |
|
11 |
|
lveclmod |
|
12 |
|
eqid |
|
13 |
|
eqid |
|
14 |
|
eqid |
|
15 |
3 12 13 14
|
lmodvscl |
|
16 |
15
|
3expb |
|
17 |
11 16
|
sylan |
|
18 |
17
|
adantlr |
|
19 |
1 13
|
tngvsca |
|
20 |
19
|
adantl |
|
21 |
20
|
oveqdr |
|
22 |
|
eqid |
|
23 |
|
eqidd |
|
24 |
1 12
|
tngsca |
|
25 |
24
|
adantl |
|
26 |
25
|
fveq2d |
|
27 |
25
|
fveq2d |
|
28 |
27
|
oveqdr |
|
29 |
|
simpl |
|
30 |
1
|
tnglvec |
|
31 |
30
|
biimpac |
|
32 |
2 5 6 10 18 21 12 22 23 26 28 29 31
|
dimpropd |
|