Step |
Hyp |
Ref |
Expression |
1 |
|
eqger.x |
|
2 |
|
eqger.r |
|
3 |
|
eqgcpbl.p |
|
4 |
|
nsgsubg |
|
5 |
4
|
adantr |
|
6 |
|
subgrcl |
|
7 |
5 6
|
syl |
|
8 |
|
simprl |
|
9 |
1
|
subgss |
|
10 |
5 9
|
syl |
|
11 |
|
eqid |
|
12 |
1 11 3 2
|
eqgval |
|
13 |
7 10 12
|
syl2anc |
|
14 |
8 13
|
mpbid |
|
15 |
14
|
simp1d |
|
16 |
|
simprr |
|
17 |
1 11 3 2
|
eqgval |
|
18 |
7 10 17
|
syl2anc |
|
19 |
16 18
|
mpbid |
|
20 |
19
|
simp1d |
|
21 |
1 3
|
grpcl |
|
22 |
7 15 20 21
|
syl3anc |
|
23 |
14
|
simp2d |
|
24 |
19
|
simp2d |
|
25 |
1 3
|
grpcl |
|
26 |
7 23 24 25
|
syl3anc |
|
27 |
1 3 11
|
grpinvadd |
|
28 |
7 15 20 27
|
syl3anc |
|
29 |
28
|
oveq1d |
|
30 |
1 11
|
grpinvcl |
|
31 |
7 20 30
|
syl2anc |
|
32 |
1 11
|
grpinvcl |
|
33 |
7 15 32
|
syl2anc |
|
34 |
1 3
|
grpass |
|
35 |
7 31 33 26 34
|
syl13anc |
|
36 |
29 35
|
eqtrd |
|
37 |
1 3
|
grpass |
|
38 |
7 33 23 24 37
|
syl13anc |
|
39 |
38
|
oveq1d |
|
40 |
1 3
|
grpcl |
|
41 |
7 33 23 40
|
syl3anc |
|
42 |
1 3
|
grpass |
|
43 |
7 41 24 31 42
|
syl13anc |
|
44 |
39 43
|
eqtr3d |
|
45 |
14
|
simp3d |
|
46 |
19
|
simp3d |
|
47 |
|
simpl |
|
48 |
1 3
|
nsgbi |
|
49 |
47 31 24 48
|
syl3anc |
|
50 |
46 49
|
mpbid |
|
51 |
3
|
subgcl |
|
52 |
5 45 50 51
|
syl3anc |
|
53 |
44 52
|
eqeltrd |
|
54 |
1 3
|
grpcl |
|
55 |
7 33 26 54
|
syl3anc |
|
56 |
1 3
|
nsgbi |
|
57 |
47 55 31 56
|
syl3anc |
|
58 |
53 57
|
mpbid |
|
59 |
36 58
|
eqeltrd |
|
60 |
1 11 3 2
|
eqgval |
|
61 |
7 10 60
|
syl2anc |
|
62 |
22 26 59 61
|
mpbir3and |
|
63 |
62
|
ex |
|