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 |
10
|
ssrab3 |
|
12 |
|
sseqin2 |
|
13 |
11 12
|
mpbi |
|
14 |
|
simpr |
|
15 |
8
|
adantr |
|
16 |
|
mptexg |
|
17 |
|
rnexg |
|
18 |
15 16 17
|
3syl |
|
19 |
|
simpr |
|
20 |
|
simpl |
|
21 |
20
|
oveq1d |
|
22 |
21 20
|
oveq12d |
|
23 |
19 22
|
mpteq12dv |
|
24 |
23
|
rneqd |
|
25 |
24 7
|
ovmpoga |
|
26 |
14 15 18 25
|
syl3anc |
|
27 |
26
|
adantr |
|
28 |
|
slwsubg |
|
29 |
8 28
|
syl |
|
30 |
29
|
adantr |
|
31 |
|
eqid |
|
32 |
1 5 6 31 10
|
conjnmz |
|
33 |
30 32
|
sylan |
|
34 |
27 33
|
eqtr4d |
|
35 |
|
simplr |
|
36 |
|
simprl |
|
37 |
26
|
adantr |
|
38 |
36 37
|
eqtr3d |
|
39 |
38
|
eleq2d |
|
40 |
|
ovex |
|
41 |
|
eqeq1 |
|
42 |
41
|
rexbidv |
|
43 |
31
|
rnmpt |
|
44 |
40 42 43
|
elab2 |
|
45 |
|
simprr |
|
46 |
2
|
ad3antrrr |
|
47 |
|
simpllr |
|
48 |
1
|
subgss |
|
49 |
29 48
|
syl |
|
50 |
49
|
ad3antrrr |
|
51 |
|
simprl |
|
52 |
50 51
|
sseldd |
|
53 |
1 5 6
|
grpaddsubass |
|
54 |
46 47 52 47 53
|
syl13anc |
|
55 |
45 54
|
eqtr2d |
|
56 |
1 6
|
grpsubcl |
|
57 |
46 52 47 56
|
syl3anc |
|
58 |
|
simplrr |
|
59 |
1 5
|
grplcan |
|
60 |
46 57 58 47 59
|
syl13anc |
|
61 |
55 60
|
mpbid |
|
62 |
1 5 6
|
grpsubadd |
|
63 |
46 52 47 58 62
|
syl13anc |
|
64 |
61 63
|
mpbid |
|
65 |
64 51
|
eqeltrd |
|
66 |
65
|
rexlimdvaa |
|
67 |
44 66
|
syl5bi |
|
68 |
|
simpr |
|
69 |
|
oveq2 |
|
70 |
69
|
oveq1d |
|
71 |
|
ovex |
|
72 |
70 31 71
|
fvmpt |
|
73 |
68 72
|
syl |
|
74 |
2
|
ad3antrrr |
|
75 |
|
simpllr |
|
76 |
|
simplrr |
|
77 |
1 5
|
grpass |
|
78 |
74 75 76 75 77
|
syl13anc |
|
79 |
78
|
oveq1d |
|
80 |
1 5
|
grpcl |
|
81 |
74 75 76 80
|
syl3anc |
|
82 |
1 5 6
|
grppncan |
|
83 |
74 81 75 82
|
syl3anc |
|
84 |
73 79 83
|
3eqtr2d |
|
85 |
|
ovex |
|
86 |
85 31
|
fnmpti |
|
87 |
|
fnfvelrn |
|
88 |
86 68 87
|
sylancr |
|
89 |
84 88
|
eqeltrrd |
|
90 |
89
|
ex |
|
91 |
67 90
|
impbid |
|
92 |
39 91
|
bitrd |
|
93 |
92
|
anassrs |
|
94 |
93
|
ralrimiva |
|
95 |
10
|
elnmz |
|
96 |
35 94 95
|
sylanbrc |
|
97 |
34 96
|
impbida |
|
98 |
97
|
rabbi2dva |
|
99 |
13 98
|
eqtr3id |
|
100 |
9 99
|
eqtr4id |
|