Step |
Hyp |
Ref |
Expression |
1 |
|
mulginvcom.b |
|
2 |
|
mulginvcom.t |
|
3 |
|
mulginvcom.i |
|
4 |
|
oveq1 |
|
5 |
|
fvoveq1 |
|
6 |
4 5
|
eqeq12d |
|
7 |
|
oveq1 |
|
8 |
|
fvoveq1 |
|
9 |
7 8
|
eqeq12d |
|
10 |
|
oveq1 |
|
11 |
|
fvoveq1 |
|
12 |
10 11
|
eqeq12d |
|
13 |
|
oveq1 |
|
14 |
|
fvoveq1 |
|
15 |
13 14
|
eqeq12d |
|
16 |
|
oveq1 |
|
17 |
|
fvoveq1 |
|
18 |
16 17
|
eqeq12d |
|
19 |
|
eqid |
|
20 |
19 3
|
grpinvid |
|
21 |
20
|
eqcomd |
|
22 |
21
|
adantr |
|
23 |
1 3
|
grpinvcl |
|
24 |
1 19 2
|
mulg0 |
|
25 |
23 24
|
syl |
|
26 |
1 19 2
|
mulg0 |
|
27 |
26
|
adantl |
|
28 |
27
|
fveq2d |
|
29 |
22 25 28
|
3eqtr4d |
|
30 |
|
oveq2 |
|
31 |
30
|
adantl |
|
32 |
|
grpmnd |
|
33 |
32
|
3ad2ant1 |
|
34 |
|
simp2 |
|
35 |
23
|
3adant2 |
|
36 |
|
eqid |
|
37 |
1 2 36
|
mulgnn0p1 |
|
38 |
33 34 35 37
|
syl3anc |
|
39 |
|
simp1 |
|
40 |
|
nn0z |
|
41 |
40
|
3ad2ant2 |
|
42 |
1 2 36
|
mulgaddcom |
|
43 |
39 41 35 42
|
syl3anc |
|
44 |
38 43
|
eqtrd |
|
45 |
44
|
adantr |
|
46 |
1 2 36
|
mulgnn0p1 |
|
47 |
32 46
|
syl3an1 |
|
48 |
47
|
fveq2d |
|
49 |
1 2
|
mulgcl |
|
50 |
40 49
|
syl3an2 |
|
51 |
1 36 3
|
grpinvadd |
|
52 |
50 51
|
syld3an2 |
|
53 |
48 52
|
eqtrd |
|
54 |
53
|
adantr |
|
55 |
31 45 54
|
3eqtr4d |
|
56 |
55
|
3exp1 |
|
57 |
56
|
com23 |
|
58 |
57
|
imp |
|
59 |
|
nnz |
|
60 |
23
|
3adant2 |
|
61 |
1 2 3
|
mulgneg |
|
62 |
60 61
|
syld3an3 |
|
63 |
62
|
adantr |
|
64 |
1 2 3
|
mulgneg |
|
65 |
64
|
adantr |
|
66 |
|
simpr |
|
67 |
65 66
|
eqtr4d |
|
68 |
67
|
fveq2d |
|
69 |
63 68
|
eqtr4d |
|
70 |
69
|
3exp1 |
|
71 |
70
|
com23 |
|
72 |
71
|
imp |
|
73 |
59 72
|
syl5 |
|
74 |
6 9 12 15 18 29 58 73
|
zindd |
|
75 |
74
|
ex |
|
76 |
75
|
com23 |
|
77 |
76
|
3imp |
|