Step |
Hyp |
Ref |
Expression |
1 |
|
clmmulg.1 |
|
2 |
|
clmmulg.2 |
|
3 |
|
clmmulg.3 |
|
4 |
|
oveq1 |
|
5 |
|
oveq1 |
|
6 |
4 5
|
eqeq12d |
|
7 |
|
oveq1 |
|
8 |
|
oveq1 |
|
9 |
7 8
|
eqeq12d |
|
10 |
|
oveq1 |
|
11 |
|
oveq1 |
|
12 |
10 11
|
eqeq12d |
|
13 |
|
oveq1 |
|
14 |
|
oveq1 |
|
15 |
13 14
|
eqeq12d |
|
16 |
|
oveq1 |
|
17 |
|
oveq1 |
|
18 |
16 17
|
eqeq12d |
|
19 |
|
eqid |
|
20 |
1 19 2
|
mulg0 |
|
21 |
20
|
adantl |
|
22 |
|
eqid |
|
23 |
1 22 3 19
|
clm0vs |
|
24 |
21 23
|
eqtr4d |
|
25 |
|
oveq1 |
|
26 |
|
clmgrp |
|
27 |
|
grpmnd |
|
28 |
26 27
|
syl |
|
29 |
28
|
ad2antrr |
|
30 |
|
simpr |
|
31 |
|
simplr |
|
32 |
|
eqid |
|
33 |
1 2 32
|
mulgnn0p1 |
|
34 |
29 30 31 33
|
syl3anc |
|
35 |
|
simpll |
|
36 |
|
eqid |
|
37 |
22 36
|
clmzss |
|
38 |
37
|
ad2antrr |
|
39 |
|
nn0z |
|
40 |
39
|
adantl |
|
41 |
38 40
|
sseldd |
|
42 |
|
1zzd |
|
43 |
38 42
|
sseldd |
|
44 |
1 22 3 36 32
|
clmvsdir |
|
45 |
35 41 43 31 44
|
syl13anc |
|
46 |
1 3
|
clmvs1 |
|
47 |
46
|
adantr |
|
48 |
47
|
oveq2d |
|
49 |
45 48
|
eqtrd |
|
50 |
34 49
|
eqeq12d |
|
51 |
25 50
|
syl5ibr |
|
52 |
51
|
ex |
|
53 |
|
fveq2 |
|
54 |
26
|
ad2antrr |
|
55 |
|
nnz |
|
56 |
55
|
adantl |
|
57 |
|
simplr |
|
58 |
|
eqid |
|
59 |
1 2 58
|
mulgneg |
|
60 |
54 56 57 59
|
syl3anc |
|
61 |
|
simpll |
|
62 |
37
|
ad2antrr |
|
63 |
62 56
|
sseldd |
|
64 |
1 22 3 58 36 61 57 63
|
clmvsneg |
|
65 |
64
|
eqcomd |
|
66 |
60 65
|
eqeq12d |
|
67 |
53 66
|
syl5ibr |
|
68 |
67
|
ex |
|
69 |
6 9 12 15 18 24 52 68
|
zindd |
|
70 |
69
|
3impia |
|
71 |
70
|
3com23 |
|