Step |
Hyp |
Ref |
Expression |
1 |
|
minvec.x |
|
2 |
|
minvec.m |
|
3 |
|
minvec.n |
|
4 |
|
minvec.u |
|
5 |
|
minvec.y |
|
6 |
|
minvec.w |
|
7 |
|
minvec.a |
|
8 |
|
minvec.j |
|
9 |
|
minvec.r |
|
10 |
|
minvec.s |
|
11 |
|
minvec.d |
|
12 |
11
|
oveqi |
|
13 |
7
|
adantr |
|
14 |
|
eqid |
|
15 |
1 14
|
lssss |
|
16 |
5 15
|
syl |
|
17 |
16
|
sselda |
|
18 |
13 17
|
ovresd |
|
19 |
12 18
|
eqtrid |
|
20 |
|
cphngp |
|
21 |
4 20
|
syl |
|
22 |
21
|
adantr |
|
23 |
|
eqid |
|
24 |
3 1 2 23
|
ngpds |
|
25 |
22 13 17 24
|
syl3anc |
|
26 |
19 25
|
eqtrd |
|
27 |
26
|
oveq1d |
|
28 |
1 2 3 4 5 6 7 8 9
|
minveclem1 |
|
29 |
28
|
adantr |
|
30 |
29
|
simp1d |
|
31 |
29
|
simp2d |
|
32 |
|
0red |
|
33 |
29
|
simp3d |
|
34 |
|
breq1 |
|
35 |
34
|
ralbidv |
|
36 |
35
|
rspcev |
|
37 |
32 33 36
|
syl2anc |
|
38 |
|
infrecl |
|
39 |
30 31 37 38
|
syl3anc |
|
40 |
10 39
|
eqeltrid |
|
41 |
40
|
resqcld |
|
42 |
41
|
recnd |
|
43 |
42
|
addridd |
|
44 |
27 43
|
breq12d |
|
45 |
|
cphlmod |
|
46 |
4 45
|
syl |
|
47 |
46
|
adantr |
|
48 |
1 2
|
lmodvsubcl |
|
49 |
47 13 17 48
|
syl3anc |
|
50 |
1 3
|
nmcl |
|
51 |
22 49 50
|
syl2anc |
|
52 |
1 3
|
nmge0 |
|
53 |
22 49 52
|
syl2anc |
|
54 |
|
infregelb |
|
55 |
30 31 37 32 54
|
syl31anc |
|
56 |
33 55
|
mpbird |
|
57 |
56 10
|
breqtrrdi |
|
58 |
51 40 53 57
|
le2sqd |
|
59 |
10
|
breq2i |
|
60 |
|
infregelb |
|
61 |
30 31 37 51 60
|
syl31anc |
|
62 |
59 61
|
bitrid |
|
63 |
44 58 62
|
3bitr2d |
|
64 |
9
|
raleqi |
|
65 |
|
fvex |
|
66 |
65
|
rgenw |
|
67 |
|
eqid |
|
68 |
|
breq2 |
|
69 |
67 68
|
ralrnmptw |
|
70 |
66 69
|
ax-mp |
|
71 |
64 70
|
bitri |
|
72 |
63 71
|
bitrdi |
|