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 |
1 2 3 4 5 6 7 8 9 10
|
sylow3lem3 |
|
12 |
|
slwsubg |
|
13 |
8 12
|
syl |
|
14 |
|
eqid |
|
15 |
10 1 5 14
|
nmznsg |
|
16 |
|
nsgsubg |
|
17 |
15 16
|
syl |
|
18 |
13 17
|
syl |
|
19 |
10 1 5
|
nmzsubg |
|
20 |
2 19
|
syl |
|
21 |
14
|
subgbas |
|
22 |
20 21
|
syl |
|
23 |
1
|
subgss |
|
24 |
20 23
|
syl |
|
25 |
3 24
|
ssfid |
|
26 |
22 25
|
eqeltrrd |
|
27 |
|
eqid |
|
28 |
27
|
lagsubg |
|
29 |
18 26 28
|
syl2anc |
|
30 |
22
|
fveq2d |
|
31 |
29 30
|
breqtrrd |
|
32 |
|
eqid |
|
33 |
32
|
subg0cl |
|
34 |
13 33
|
syl |
|
35 |
34
|
ne0d |
|
36 |
1
|
subgss |
|
37 |
13 36
|
syl |
|
38 |
3 37
|
ssfid |
|
39 |
|
hashnncl |
|
40 |
38 39
|
syl |
|
41 |
35 40
|
mpbird |
|
42 |
41
|
nnzd |
|
43 |
|
hashcl |
|
44 |
25 43
|
syl |
|
45 |
44
|
nn0zd |
|
46 |
|
pwfi |
|
47 |
3 46
|
sylib |
|
48 |
|
eqid |
|
49 |
1 48
|
eqger |
|
50 |
20 49
|
syl |
|
51 |
50
|
qsss |
|
52 |
47 51
|
ssfid |
|
53 |
|
hashcl |
|
54 |
52 53
|
syl |
|
55 |
54
|
nn0zd |
|
56 |
|
dvdscmul |
|
57 |
42 45 55 56
|
syl3anc |
|
58 |
31 57
|
mpd |
|
59 |
|
hashcl |
|
60 |
3 59
|
syl |
|
61 |
60
|
nn0cnd |
|
62 |
41
|
nncnd |
|
63 |
41
|
nnne0d |
|
64 |
61 62 63
|
divcan1d |
|
65 |
1 48 20 3
|
lagsubg2 |
|
66 |
64 65
|
eqtrd |
|
67 |
58 66
|
breqtrrd |
|
68 |
1
|
lagsubg |
|
69 |
13 3 68
|
syl2anc |
|
70 |
60
|
nn0zd |
|
71 |
|
dvdsval2 |
|
72 |
42 63 70 71
|
syl3anc |
|
73 |
69 72
|
mpbid |
|
74 |
|
dvdsmulcr |
|
75 |
55 73 42 63 74
|
syl112anc |
|
76 |
67 75
|
mpbid |
|
77 |
1 3 8
|
slwhash |
|
78 |
77
|
oveq2d |
|
79 |
76 78
|
breqtrd |
|
80 |
11 79
|
eqbrtrd |
|