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