Step |
Hyp |
Ref |
Expression |
1 |
|
subgga.1 |
|
2 |
|
subgga.2 |
|
3 |
|
subgga.3 |
|
4 |
|
subgga.4 |
|
5 |
3
|
subggrp |
|
6 |
1
|
fvexi |
|
7 |
5 6
|
jctir |
|
8 |
|
subgrcl |
|
9 |
8
|
adantr |
|
10 |
1
|
subgss |
|
11 |
10
|
sselda |
|
12 |
11
|
adantrr |
|
13 |
|
simprr |
|
14 |
1 2
|
grpcl |
|
15 |
9 12 13 14
|
syl3anc |
|
16 |
15
|
ralrimivva |
|
17 |
4
|
fmpo |
|
18 |
16 17
|
sylib |
|
19 |
3
|
subgbas |
|
20 |
19
|
xpeq1d |
|
21 |
20
|
feq2d |
|
22 |
18 21
|
mpbid |
|
23 |
|
eqid |
|
24 |
23
|
subg0cl |
|
25 |
|
oveq12 |
|
26 |
|
ovex |
|
27 |
25 4 26
|
ovmpoa |
|
28 |
24 27
|
sylan |
|
29 |
3 23
|
subg0 |
|
30 |
29
|
oveq1d |
|
31 |
30
|
adantr |
|
32 |
1 2 23
|
grplid |
|
33 |
8 32
|
sylan |
|
34 |
28 31 33
|
3eqtr3d |
|
35 |
8
|
ad2antrr |
|
36 |
10
|
ad2antrr |
|
37 |
|
simprl |
|
38 |
36 37
|
sseldd |
|
39 |
|
simprr |
|
40 |
36 39
|
sseldd |
|
41 |
|
simplr |
|
42 |
1 2
|
grpass |
|
43 |
35 38 40 41 42
|
syl13anc |
|
44 |
1 2
|
grpcl |
|
45 |
35 40 41 44
|
syl3anc |
|
46 |
|
oveq12 |
|
47 |
|
ovex |
|
48 |
46 4 47
|
ovmpoa |
|
49 |
37 45 48
|
syl2anc |
|
50 |
43 49
|
eqtr4d |
|
51 |
2
|
subgcl |
|
52 |
51
|
3expb |
|
53 |
52
|
adantlr |
|
54 |
|
oveq12 |
|
55 |
|
ovex |
|
56 |
54 4 55
|
ovmpoa |
|
57 |
53 41 56
|
syl2anc |
|
58 |
|
oveq12 |
|
59 |
|
ovex |
|
60 |
58 4 59
|
ovmpoa |
|
61 |
39 41 60
|
syl2anc |
|
62 |
61
|
oveq2d |
|
63 |
50 57 62
|
3eqtr4d |
|
64 |
63
|
ralrimivva |
|
65 |
3 2
|
ressplusg |
|
66 |
65
|
oveqd |
|
67 |
66
|
oveq1d |
|
68 |
67
|
eqeq1d |
|
69 |
19 68
|
raleqbidv |
|
70 |
19 69
|
raleqbidv |
|
71 |
70
|
biimpa |
|
72 |
64 71
|
syldan |
|
73 |
34 72
|
jca |
|
74 |
73
|
ralrimiva |
|
75 |
22 74
|
jca |
|
76 |
|
eqid |
|
77 |
|
eqid |
|
78 |
|
eqid |
|
79 |
76 77 78
|
isga |
|
80 |
7 75 79
|
sylanbrc |
|