Step |
Hyp |
Ref |
Expression |
1 |
|
sylow1.x |
|
2 |
|
sylow1.g |
|
3 |
|
sylow1.f |
|
4 |
|
sylow1.p |
|
5 |
|
sylow1.n |
|
6 |
|
sylow1.d |
|
7 |
|
sylow1lem.a |
|
8 |
|
sylow1lem.s |
|
9 |
|
sylow1lem.m |
|
10 |
|
sylow1lem3.1 |
|
11 |
|
sylow1lem4.b |
|
12 |
|
sylow1lem4.h |
|
13 |
|
fveqeq2 |
|
14 |
13 8
|
elrab2 |
|
15 |
11 14
|
sylib |
|
16 |
15
|
simprd |
|
17 |
|
prmnn |
|
18 |
4 17
|
syl |
|
19 |
18 5
|
nnexpcld |
|
20 |
16 19
|
eqeltrd |
|
21 |
20
|
nnne0d |
|
22 |
|
hasheq0 |
|
23 |
22
|
necon3bid |
|
24 |
11 23
|
syl |
|
25 |
21 24
|
mpbid |
|
26 |
|
n0 |
|
27 |
25 26
|
sylib |
|
28 |
11
|
adantr |
|
29 |
|
simplr |
|
30 |
|
oveq2 |
|
31 |
|
eqid |
|
32 |
|
ovex |
|
33 |
30 31 32
|
fvmpt |
|
34 |
29 33
|
syl |
|
35 |
|
ovex |
|
36 |
35 31
|
fnmpti |
|
37 |
|
fnfvelrn |
|
38 |
36 29 37
|
sylancr |
|
39 |
34 38
|
eqeltrrd |
|
40 |
12
|
ssrab3 |
|
41 |
|
simpr |
|
42 |
40 41
|
sselid |
|
43 |
11
|
ad2antrr |
|
44 |
|
mptexg |
|
45 |
|
rnexg |
|
46 |
43 44 45
|
3syl |
|
47 |
|
simpr |
|
48 |
|
simpl |
|
49 |
48
|
oveq1d |
|
50 |
47 49
|
mpteq12dv |
|
51 |
50
|
rneqd |
|
52 |
51 9
|
ovmpoga |
|
53 |
42 43 46 52
|
syl3anc |
|
54 |
39 53
|
eleqtrrd |
|
55 |
|
oveq1 |
|
56 |
55
|
eqeq1d |
|
57 |
56 12
|
elrab2 |
|
58 |
57
|
simprbi |
|
59 |
58
|
adantl |
|
60 |
54 59
|
eleqtrd |
|
61 |
60
|
ex |
|
62 |
2
|
ad2antrr |
|
63 |
|
simprl |
|
64 |
40 63
|
sselid |
|
65 |
|
simprr |
|
66 |
40 65
|
sselid |
|
67 |
15
|
simpld |
|
68 |
67
|
elpwid |
|
69 |
68
|
sselda |
|
70 |
69
|
adantr |
|
71 |
1 7
|
grprcan |
|
72 |
62 64 66 70 71
|
syl13anc |
|
73 |
72
|
ex |
|
74 |
61 73
|
dom2d |
|
75 |
28 74
|
mpd |
|
76 |
27 75
|
exlimddv |
|
77 |
|
ssfi |
|
78 |
3 40 77
|
sylancl |
|
79 |
3 68
|
ssfid |
|
80 |
|
hashdom |
|
81 |
78 79 80
|
syl2anc |
|
82 |
76 81
|
mpbird |
|
83 |
82 16
|
breqtrd |
|