Step |
Hyp |
Ref |
Expression |
1 |
|
mulgneg2.b |
|
2 |
|
mulgneg2.m |
|
3 |
|
mulgneg2.i |
|
4 |
|
negeq |
|
5 |
|
neg0 |
|
6 |
4 5
|
eqtrdi |
|
7 |
6
|
oveq1d |
|
8 |
|
oveq1 |
|
9 |
7 8
|
eqeq12d |
|
10 |
|
negeq |
|
11 |
10
|
oveq1d |
|
12 |
|
oveq1 |
|
13 |
11 12
|
eqeq12d |
|
14 |
|
negeq |
|
15 |
14
|
oveq1d |
|
16 |
|
oveq1 |
|
17 |
15 16
|
eqeq12d |
|
18 |
|
negeq |
|
19 |
18
|
oveq1d |
|
20 |
|
oveq1 |
|
21 |
19 20
|
eqeq12d |
|
22 |
|
negeq |
|
23 |
22
|
oveq1d |
|
24 |
|
oveq1 |
|
25 |
23 24
|
eqeq12d |
|
26 |
|
eqid |
|
27 |
1 26 2
|
mulg0 |
|
28 |
27
|
adantl |
|
29 |
1 3
|
grpinvcl |
|
30 |
1 26 2
|
mulg0 |
|
31 |
29 30
|
syl |
|
32 |
28 31
|
eqtr4d |
|
33 |
|
oveq1 |
|
34 |
|
nn0cn |
|
35 |
34
|
adantl |
|
36 |
|
ax-1cn |
|
37 |
|
negdi |
|
38 |
35 36 37
|
sylancl |
|
39 |
38
|
oveq1d |
|
40 |
|
simpll |
|
41 |
|
nn0negz |
|
42 |
41
|
adantl |
|
43 |
|
1z |
|
44 |
|
znegcl |
|
45 |
43 44
|
mp1i |
|
46 |
|
simplr |
|
47 |
|
eqid |
|
48 |
1 2 47
|
mulgdir |
|
49 |
40 42 45 46 48
|
syl13anc |
|
50 |
1 2 3
|
mulgm1 |
|
51 |
50
|
adantr |
|
52 |
51
|
oveq2d |
|
53 |
39 49 52
|
3eqtrd |
|
54 |
|
grpmnd |
|
55 |
54
|
ad2antrr |
|
56 |
|
simpr |
|
57 |
29
|
adantr |
|
58 |
1 2 47
|
mulgnn0p1 |
|
59 |
55 56 57 58
|
syl3anc |
|
60 |
53 59
|
eqeq12d |
|
61 |
33 60
|
syl5ibr |
|
62 |
61
|
ex |
|
63 |
|
fveq2 |
|
64 |
|
simpll |
|
65 |
|
nnnegz |
|
66 |
65
|
adantl |
|
67 |
|
simplr |
|
68 |
1 2 3
|
mulgneg |
|
69 |
64 66 67 68
|
syl3anc |
|
70 |
|
id |
|
71 |
1 2 3
|
mulgnegnn |
|
72 |
70 29 71
|
syl2anr |
|
73 |
69 72
|
eqeq12d |
|
74 |
63 73
|
syl5ibr |
|
75 |
74
|
ex |
|
76 |
9 13 17 21 25 32 62 75
|
zindd |
|
77 |
76
|
3impia |
|
78 |
77
|
3com23 |
|