Step |
Hyp |
Ref |
Expression |
1 |
|
sylow3.x |
|
2 |
|
sylow3.g |
|
3 |
|
sylow3.xf |
|
4 |
|
sylow3.p |
|
5 |
|
sylow3lem1.a |
|
6 |
|
sylow3lem1.d |
|
7 |
|
sylow3lem1.m |
|
8 |
|
sylow3lem2.k |
|
9 |
|
sylow3lem2.h |
|
10 |
|
sylow3lem2.n |
|
11 |
|
pwfi |
|
12 |
3 11
|
sylib |
|
13 |
|
slwsubg |
|
14 |
1
|
subgss |
|
15 |
13 14
|
syl |
|
16 |
13 15
|
elpwd |
|
17 |
16
|
ssriv |
|
18 |
|
ssfi |
|
19 |
12 17 18
|
sylancl |
|
20 |
|
hashcl |
|
21 |
19 20
|
syl |
|
22 |
21
|
nn0cnd |
|
23 |
10 1 5
|
nmzsubg |
|
24 |
|
eqid |
|
25 |
1 24
|
eqger |
|
26 |
2 23 25
|
3syl |
|
27 |
26
|
qsss |
|
28 |
12 27
|
ssfid |
|
29 |
|
hashcl |
|
30 |
28 29
|
syl |
|
31 |
30
|
nn0cnd |
|
32 |
2 23
|
syl |
|
33 |
|
eqid |
|
34 |
33
|
subg0cl |
|
35 |
|
ne0i |
|
36 |
32 34 35
|
3syl |
|
37 |
1
|
subgss |
|
38 |
2 23 37
|
3syl |
|
39 |
3 38
|
ssfid |
|
40 |
|
hashnncl |
|
41 |
39 40
|
syl |
|
42 |
36 41
|
mpbird |
|
43 |
42
|
nncnd |
|
44 |
42
|
nnne0d |
|
45 |
1 2 3 4 5 6 7
|
sylow3lem1 |
|
46 |
|
eqid |
|
47 |
|
eqid |
|
48 |
1 9 46 47
|
orbsta2 |
|
49 |
45 8 3 48
|
syl21anc |
|
50 |
1 24 32 3
|
lagsubg2 |
|
51 |
47 1
|
gaorber |
|
52 |
45 51
|
syl |
|
53 |
52
|
ecss |
|
54 |
8
|
adantr |
|
55 |
|
simpr |
|
56 |
3
|
adantr |
|
57 |
1 56 55 54 5 6
|
sylow2 |
|
58 |
|
eqcom |
|
59 |
|
simpr |
|
60 |
54
|
adantr |
|
61 |
|
mptexg |
|
62 |
|
rnexg |
|
63 |
60 61 62
|
3syl |
|
64 |
|
simpr |
|
65 |
|
simpl |
|
66 |
65
|
oveq1d |
|
67 |
66 65
|
oveq12d |
|
68 |
64 67
|
mpteq12dv |
|
69 |
68
|
rneqd |
|
70 |
69 7
|
ovmpoga |
|
71 |
59 60 63 70
|
syl3anc |
|
72 |
71
|
eqeq2d |
|
73 |
58 72
|
syl5bb |
|
74 |
73
|
rexbidva |
|
75 |
57 74
|
mpbird |
|
76 |
47
|
gaorb |
|
77 |
54 55 75 76
|
syl3anbrc |
|
78 |
|
elecg |
|
79 |
55 54 78
|
syl2anc |
|
80 |
77 79
|
mpbird |
|
81 |
53 80
|
eqelssd |
|
82 |
81
|
fveq2d |
|
83 |
1 2 3 4 5 6 7 8 9 10
|
sylow3lem2 |
|
84 |
83
|
fveq2d |
|
85 |
82 84
|
oveq12d |
|
86 |
49 50 85
|
3eqtr3rd |
|
87 |
22 31 43 44 86
|
mulcan2ad |
|