Step |
Hyp |
Ref |
Expression |
1 |
|
brgic |
|
2 |
|
n0 |
|
3 |
|
gimghm |
|
4 |
|
ghmgrp1 |
|
5 |
3 4
|
syl |
|
6 |
|
ghmgrp2 |
|
7 |
3 6
|
syl |
|
8 |
5 7
|
2thd |
|
9 |
|
grpmnd |
|
10 |
5 9
|
syl |
|
11 |
|
grpmnd |
|
12 |
7 11
|
syl |
|
13 |
10 12
|
2thd |
|
14 |
|
eqid |
|
15 |
|
eqid |
|
16 |
14 15
|
gimf1o |
|
17 |
|
f1of1 |
|
18 |
16 17
|
syl |
|
19 |
18
|
adantr |
|
20 |
5
|
adantr |
|
21 |
|
simprl |
|
22 |
|
simprr |
|
23 |
|
eqid |
|
24 |
14 23
|
grpcl |
|
25 |
20 21 22 24
|
syl3anc |
|
26 |
14 23
|
grpcl |
|
27 |
20 22 21 26
|
syl3anc |
|
28 |
|
f1fveq |
|
29 |
19 25 27 28
|
syl12anc |
|
30 |
3
|
adantr |
|
31 |
|
eqid |
|
32 |
14 23 31
|
ghmlin |
|
33 |
30 21 22 32
|
syl3anc |
|
34 |
14 23 31
|
ghmlin |
|
35 |
30 22 21 34
|
syl3anc |
|
36 |
33 35
|
eqeq12d |
|
37 |
29 36
|
bitr3d |
|
38 |
37
|
2ralbidva |
|
39 |
|
f1ofo |
|
40 |
|
foima |
|
41 |
39 40
|
syl |
|
42 |
16 41
|
syl |
|
43 |
42
|
raleqdv |
|
44 |
|
f1ofn |
|
45 |
16 44
|
syl |
|
46 |
|
ssid |
|
47 |
|
oveq2 |
|
48 |
|
oveq1 |
|
49 |
47 48
|
eqeq12d |
|
50 |
49
|
ralima |
|
51 |
45 46 50
|
sylancl |
|
52 |
43 51
|
bitr3d |
|
53 |
52
|
ralbidv |
|
54 |
38 53
|
bitr4d |
|
55 |
42
|
raleqdv |
|
56 |
|
oveq1 |
|
57 |
|
oveq2 |
|
58 |
56 57
|
eqeq12d |
|
59 |
58
|
ralbidv |
|
60 |
59
|
ralima |
|
61 |
45 46 60
|
sylancl |
|
62 |
55 61
|
bitr3d |
|
63 |
54 62
|
bitr4d |
|
64 |
13 63
|
anbi12d |
|
65 |
14 23
|
iscmn |
|
66 |
15 31
|
iscmn |
|
67 |
64 65 66
|
3bitr4g |
|
68 |
8 67
|
anbi12d |
|
69 |
|
isabl |
|
70 |
|
isabl |
|
71 |
68 69 70
|
3bitr4g |
|
72 |
71
|
exlimiv |
|
73 |
2 72
|
sylbi |
|
74 |
1 73
|
sylbi |
|