Step |
Hyp |
Ref |
Expression |
1 |
|
prjsprel.1 |
|
2 |
|
prjspertr.b |
|
3 |
|
prjspertr.s |
|
4 |
|
prjspertr.x |
|
5 |
|
prjspertr.k |
|
6 |
|
simpllr |
|
7 |
1
|
prjsprel |
|
8 |
|
pm3.22 |
|
9 |
8
|
adantr |
|
10 |
7 9
|
sylbi |
|
11 |
6 10
|
syl |
|
12 |
|
simplll |
|
13 |
3
|
lvecdrng |
|
14 |
12 13
|
syl |
|
15 |
|
simplr |
|
16 |
|
simpll |
|
17 |
7 16
|
sylbi |
|
18 |
|
eldifsni |
|
19 |
18 2
|
eleq2s |
|
20 |
6 17 19
|
3syl |
|
21 |
|
simplr |
|
22 |
|
simpr |
|
23 |
22
|
oveq1d |
|
24 |
|
lveclmod |
|
25 |
24
|
ad4antr |
|
26 |
|
simplr |
|
27 |
7 26
|
sylbi |
|
28 |
|
eldifi |
|
29 |
28 2
|
eleq2s |
|
30 |
6 27 29
|
3syl |
|
31 |
30
|
adantr |
|
32 |
|
eqid |
|
33 |
|
eqid |
|
34 |
|
eqid |
|
35 |
32 3 4 33 34
|
lmod0vs |
|
36 |
25 31 35
|
syl2anc |
|
37 |
21 23 36
|
3eqtrd |
|
38 |
20 37
|
mteqand |
|
39 |
|
eqid |
|
40 |
5 33 39
|
drnginvrcl |
|
41 |
14 15 38 40
|
syl3anc |
|
42 |
|
oveq1 |
|
43 |
42
|
eqeq2d |
|
44 |
43
|
adantl |
|
45 |
|
simpr |
|
46 |
|
nelsn |
|
47 |
38 46
|
syl |
|
48 |
15 47
|
eldifd |
|
49 |
|
eldifi |
|
50 |
49 2
|
eleq2s |
|
51 |
6 17 50
|
3syl |
|
52 |
32 4 3 5 33 39 12 48 51 30
|
lvecinv |
|
53 |
45 52
|
mpbid |
|
54 |
41 44 53
|
rspcedvd |
|
55 |
1
|
prjsprel |
|
56 |
11 54 55
|
sylanbrc |
|
57 |
|
simpr |
|
58 |
7 57
|
sylbi |
|
59 |
58
|
adantl |
|
60 |
56 59
|
r19.29a |
|