Step |
Hyp |
Ref |
Expression |
1 |
|
grprcan.b |
|
2 |
|
grprcan.p |
|
3 |
|
eqid |
|
4 |
1 2 3
|
grpinvex |
|
5 |
4
|
3ad2antr3 |
|
6 |
|
simprr |
|
7 |
6
|
oveq1d |
|
8 |
|
simpll |
|
9 |
1 2
|
grpass |
|
10 |
8 9
|
sylan |
|
11 |
|
simplr1 |
|
12 |
|
simplr3 |
|
13 |
|
simprll |
|
14 |
10 11 12 13
|
caovassd |
|
15 |
|
simplr2 |
|
16 |
10 15 12 13
|
caovassd |
|
17 |
7 14 16
|
3eqtr3d |
|
18 |
1 2
|
grpcl |
|
19 |
8 18
|
syl3an1 |
|
20 |
1 3
|
grpidcl |
|
21 |
8 20
|
syl |
|
22 |
1 2 3
|
grplid |
|
23 |
8 22
|
sylan |
|
24 |
1 2 3
|
grpinvex |
|
25 |
8 24
|
sylan |
|
26 |
|
simpr |
|
27 |
13
|
adantr |
|
28 |
|
simprlr |
|
29 |
28
|
adantr |
|
30 |
19 21 23 10 25 26 27 29
|
grpinva |
|
31 |
12 30
|
mpdan |
|
32 |
31
|
oveq2d |
|
33 |
31
|
oveq2d |
|
34 |
17 32 33
|
3eqtr3d |
|
35 |
1 2 3 8 11
|
grpridd |
|
36 |
1 2 3 8 15
|
grpridd |
|
37 |
34 35 36
|
3eqtr3d |
|
38 |
37
|
expr |
|
39 |
5 38
|
rexlimddv |
|
40 |
|
oveq1 |
|
41 |
39 40
|
impbid1 |
|