Step |
Hyp |
Ref |
Expression |
1 |
|
gaorb.1 |
|
2 |
|
gaorber.2 |
|
3 |
1
|
relopabi |
|
4 |
3
|
a1i |
|
5 |
|
simpr |
|
6 |
1
|
gaorb |
|
7 |
5 6
|
sylib |
|
8 |
7
|
simp2d |
|
9 |
7
|
simp1d |
|
10 |
7
|
simp3d |
|
11 |
|
simpll |
|
12 |
|
simpr |
|
13 |
9
|
adantr |
|
14 |
8
|
adantr |
|
15 |
|
eqid |
|
16 |
2 15
|
gacan |
|
17 |
11 12 13 14 16
|
syl13anc |
|
18 |
|
gagrp |
|
19 |
18
|
adantr |
|
20 |
2 15
|
grpinvcl |
|
21 |
19 20
|
sylan |
|
22 |
|
oveq1 |
|
23 |
22
|
eqeq1d |
|
24 |
23
|
rspcev |
|
25 |
24
|
ex |
|
26 |
21 25
|
syl |
|
27 |
17 26
|
sylbid |
|
28 |
27
|
rexlimdva |
|
29 |
10 28
|
mpd |
|
30 |
1
|
gaorb |
|
31 |
8 9 29 30
|
syl3anbrc |
|
32 |
9
|
adantrr |
|
33 |
|
simprr |
|
34 |
1
|
gaorb |
|
35 |
33 34
|
sylib |
|
36 |
35
|
simp2d |
|
37 |
10
|
adantrr |
|
38 |
35
|
simp3d |
|
39 |
|
reeanv |
|
40 |
18
|
ad2antrr |
|
41 |
|
simprlr |
|
42 |
|
simprll |
|
43 |
|
eqid |
|
44 |
2 43
|
grpcl |
|
45 |
40 41 42 44
|
syl3anc |
|
46 |
|
simpll |
|
47 |
32
|
adantr |
|
48 |
2 43
|
gaass |
|
49 |
46 41 42 47 48
|
syl13anc |
|
50 |
|
simprrl |
|
51 |
50
|
oveq2d |
|
52 |
|
simprrr |
|
53 |
49 51 52
|
3eqtrd |
|
54 |
|
oveq1 |
|
55 |
54
|
eqeq1d |
|
56 |
55
|
rspcev |
|
57 |
45 53 56
|
syl2anc |
|
58 |
57
|
expr |
|
59 |
58
|
rexlimdvva |
|
60 |
39 59
|
syl5bir |
|
61 |
37 38 60
|
mp2and |
|
62 |
1
|
gaorb |
|
63 |
32 36 61 62
|
syl3anbrc |
|
64 |
18
|
adantr |
|
65 |
|
eqid |
|
66 |
2 65
|
grpidcl |
|
67 |
64 66
|
syl |
|
68 |
65
|
gagrpid |
|
69 |
|
oveq1 |
|
70 |
69
|
eqeq1d |
|
71 |
70
|
rspcev |
|
72 |
67 68 71
|
syl2anc |
|
73 |
72
|
ex |
|
74 |
73
|
pm4.71rd |
|
75 |
|
df-3an |
|
76 |
|
anidm |
|
77 |
76
|
anbi2ci |
|
78 |
75 77
|
bitri |
|
79 |
74 78
|
bitr4di |
|
80 |
1
|
gaorb |
|
81 |
79 80
|
bitr4di |
|
82 |
4 31 63 81
|
iserd |
|