Step |
Hyp |
Ref |
Expression |
1 |
|
sylow3.x |
|
2 |
|
sylow3.g |
|
3 |
|
sylow3.xf |
|
4 |
|
sylow3.p |
|
5 |
|
sylow3lem5.a |
|
6 |
|
sylow3lem5.d |
|
7 |
|
sylow3lem5.k |
|
8 |
|
sylow3lem5.m |
|
9 |
|
sylow3lem6.n |
|
10 |
|
eqid |
|
11 |
1 2 3 4 5 6 7 8
|
sylow3lem5 |
|
12 |
|
eqid |
|
13 |
12
|
slwpgp |
|
14 |
7 13
|
syl |
|
15 |
|
slwsubg |
|
16 |
7 15
|
syl |
|
17 |
12
|
subgbas |
|
18 |
16 17
|
syl |
|
19 |
1
|
subgss |
|
20 |
16 19
|
syl |
|
21 |
3 20
|
ssfid |
|
22 |
18 21
|
eqeltrrd |
|
23 |
|
pwfi |
|
24 |
3 23
|
sylib |
|
25 |
|
slwsubg |
|
26 |
1
|
subgss |
|
27 |
25 26
|
syl |
|
28 |
25 27
|
elpwd |
|
29 |
28
|
ssriv |
|
30 |
|
ssfi |
|
31 |
24 29 30
|
sylancl |
|
32 |
|
eqid |
|
33 |
|
eqid |
|
34 |
10 11 14 22 31 32 33
|
sylow2a |
|
35 |
|
eqcom |
|
36 |
20
|
adantr |
|
37 |
36
|
sselda |
|
38 |
37
|
biantrurd |
|
39 |
35 38
|
syl5bb |
|
40 |
|
simpr |
|
41 |
|
simplr |
|
42 |
|
simpr |
|
43 |
|
simpl |
|
44 |
43
|
oveq1d |
|
45 |
44 43
|
oveq12d |
|
46 |
42 45
|
mpteq12dv |
|
47 |
46
|
rneqd |
|
48 |
|
vex |
|
49 |
48
|
mptex |
|
50 |
49
|
rnex |
|
51 |
47 8 50
|
ovmpoa |
|
52 |
40 41 51
|
syl2anc |
|
53 |
52
|
eqeq1d |
|
54 |
|
slwsubg |
|
55 |
54
|
ad2antlr |
|
56 |
|
eqid |
|
57 |
1 5 6 56 9
|
conjnmzb |
|
58 |
55 57
|
syl |
|
59 |
39 53 58
|
3bitr4d |
|
60 |
59
|
ralbidva |
|
61 |
|
dfss3 |
|
62 |
60 61
|
bitr4di |
|
63 |
18
|
adantr |
|
64 |
63
|
raleqdv |
|
65 |
|
eqid |
|
66 |
2
|
ad2antrr |
|
67 |
9 1 5
|
nmzsubg |
|
68 |
66 67
|
syl |
|
69 |
|
eqid |
|
70 |
69
|
subgbas |
|
71 |
68 70
|
syl |
|
72 |
3
|
ad2antrr |
|
73 |
1
|
subgss |
|
74 |
68 73
|
syl |
|
75 |
72 74
|
ssfid |
|
76 |
71 75
|
eqeltrrd |
|
77 |
7
|
ad2antrr |
|
78 |
|
simpr |
|
79 |
69
|
subgslw |
|
80 |
68 77 78 79
|
syl3anc |
|
81 |
|
simplr |
|
82 |
54
|
ad2antlr |
|
83 |
9 1 5
|
ssnmz |
|
84 |
82 83
|
syl |
|
85 |
69
|
subgslw |
|
86 |
68 81 84 85
|
syl3anc |
|
87 |
1
|
fvexi |
|
88 |
9 87
|
rabex2 |
|
89 |
69 5
|
ressplusg |
|
90 |
88 89
|
ax-mp |
|
91 |
|
eqid |
|
92 |
65 76 80 86 90 91
|
sylow2 |
|
93 |
9 1 5 69
|
nmznsg |
|
94 |
82 93
|
syl |
|
95 |
|
eqid |
|
96 |
65 90 91 95
|
conjnsg |
|
97 |
94 96
|
sylan |
|
98 |
|
eqeq2 |
|
99 |
97 98
|
syl5ibrcom |
|
100 |
99
|
rexlimdva |
|
101 |
92 100
|
mpd |
|
102 |
|
simpr |
|
103 |
16
|
ad2antrr |
|
104 |
102 103
|
eqeltrd |
|
105 |
104 83
|
syl |
|
106 |
102 105
|
eqsstrrd |
|
107 |
101 106
|
impbida |
|
108 |
62 64 107
|
3bitr3d |
|
109 |
108
|
rabbidva |
|
110 |
|
rabsn |
|
111 |
7 110
|
syl |
|
112 |
109 111
|
eqtrd |
|
113 |
112
|
fveq2d |
|
114 |
|
hashsng |
|
115 |
7 114
|
syl |
|
116 |
113 115
|
eqtrd |
|
117 |
116
|
oveq2d |
|
118 |
34 117
|
breqtrd |
|
119 |
|
prmnn |
|
120 |
4 119
|
syl |
|
121 |
|
hashcl |
|
122 |
31 121
|
syl |
|
123 |
122
|
nn0zd |
|
124 |
|
1zzd |
|
125 |
|
moddvds |
|
126 |
120 123 124 125
|
syl3anc |
|
127 |
118 126
|
mpbird |
|
128 |
|
prmuz2 |
|
129 |
|
eluz2b2 |
|
130 |
|
nnre |
|
131 |
|
1mod |
|
132 |
130 131
|
sylan |
|
133 |
129 132
|
sylbi |
|
134 |
4 128 133
|
3syl |
|
135 |
127 134
|
eqtrd |
|