Step |
Hyp |
Ref |
Expression |
1 |
|
conjghm.x |
|
2 |
|
conjghm.p |
|
3 |
|
conjghm.m |
|
4 |
|
conjsubg.f |
|
5 |
|
conjnmz.1 |
|
6 |
|
subgrcl |
|
7 |
6
|
ad2antrr |
|
8 |
|
eqid |
|
9 |
5
|
ssrab3 |
|
10 |
|
simplr |
|
11 |
9 10
|
sselid |
|
12 |
1 8 7 11
|
grpinvcld |
|
13 |
1
|
subgss |
|
14 |
13
|
adantr |
|
15 |
14
|
sselda |
|
16 |
1 2 7 12 15 11
|
grpassd |
|
17 |
|
eqid |
|
18 |
1 2 17 8 7 11
|
grprinvd |
|
19 |
18
|
oveq1d |
|
20 |
1 2 7 11 12 15
|
grpassd |
|
21 |
1 2 17 7 15
|
grplidd |
|
22 |
19 20 21
|
3eqtr3d |
|
23 |
|
simpr |
|
24 |
22 23
|
eqeltrd |
|
25 |
1 2 7 12 15
|
grpcld |
|
26 |
5
|
nmzbi |
|
27 |
10 25 26
|
syl2anc |
|
28 |
24 27
|
mpbid |
|
29 |
16 28
|
eqeltrrd |
|
30 |
|
oveq2 |
|
31 |
30
|
oveq1d |
|
32 |
|
ovex |
|
33 |
31 4 32
|
fvmpt |
|
34 |
29 33
|
syl |
|
35 |
18
|
oveq1d |
|
36 |
1 2 7 15 11
|
grpcld |
|
37 |
1 2 7 11 12 36
|
grpassd |
|
38 |
1 2 17 7 36
|
grplidd |
|
39 |
35 37 38
|
3eqtr3d |
|
40 |
39
|
oveq1d |
|
41 |
1 2 3
|
grppncan |
|
42 |
7 15 11 41
|
syl3anc |
|
43 |
34 40 42
|
3eqtrd |
|
44 |
|
ovex |
|
45 |
44 4
|
fnmpti |
|
46 |
|
fnfvelrn |
|
47 |
45 29 46
|
sylancr |
|
48 |
43 47
|
eqeltrrd |
|
49 |
48
|
ex |
|
50 |
49
|
ssrdv |
|
51 |
6
|
ad2antrr |
|
52 |
|
simplr |
|
53 |
9 52
|
sselid |
|
54 |
14
|
sselda |
|
55 |
1 2 3
|
grpaddsubass |
|
56 |
51 53 54 53 55
|
syl13anc |
|
57 |
1 2 3
|
grpnpcan |
|
58 |
51 54 53 57
|
syl3anc |
|
59 |
|
simpr |
|
60 |
58 59
|
eqeltrd |
|
61 |
1 3
|
grpsubcl |
|
62 |
51 54 53 61
|
syl3anc |
|
63 |
5
|
nmzbi |
|
64 |
52 62 63
|
syl2anc |
|
65 |
60 64
|
mpbird |
|
66 |
56 65
|
eqeltrd |
|
67 |
66 4
|
fmptd |
|
68 |
67
|
frnd |
|
69 |
50 68
|
eqssd |
|