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 |
|
slwsubg |
|
10 |
7 9
|
syl |
|
11 |
1
|
subgss |
|
12 |
10 11
|
syl |
|
13 |
|
ssid |
|
14 |
|
resmpo |
|
15 |
12 13 14
|
sylancl |
|
16 |
15 8
|
eqtr4di |
|
17 |
|
oveq2 |
|
18 |
17
|
oveq1d |
|
19 |
18
|
cbvmptv |
|
20 |
|
oveq1 |
|
21 |
|
id |
|
22 |
20 21
|
oveq12d |
|
23 |
22
|
mpteq2dv |
|
24 |
19 23
|
eqtrid |
|
25 |
24
|
rneqd |
|
26 |
|
mpteq1 |
|
27 |
26
|
rneqd |
|
28 |
25 27
|
cbvmpov |
|
29 |
1 2 3 4 5 6 28
|
sylow3lem1 |
|
30 |
|
eqid |
|
31 |
30
|
gasubg |
|
32 |
29 10 31
|
syl2anc |
|
33 |
16 32
|
eqeltrrd |
|