Step |
Hyp |
Ref |
Expression |
1 |
|
grplsmid.p |
|
2 |
|
subgrcl |
|
3 |
2
|
adantr |
|
4 |
|
eqid |
|
5 |
4
|
subgss |
|
6 |
5
|
sselda |
|
7 |
6
|
snssd |
|
8 |
5
|
adantr |
|
9 |
|
eqid |
|
10 |
4 9 1
|
lsmelvalx |
|
11 |
3 7 8 10
|
syl3anc |
|
12 |
|
oveq1 |
|
13 |
12
|
eqeq2d |
|
14 |
13
|
rexbidv |
|
15 |
14
|
rexsng |
|
16 |
15
|
adantl |
|
17 |
|
simpr |
|
18 |
9
|
subgcl |
|
19 |
18
|
ad4ant123 |
|
20 |
17 19
|
eqeltrd |
|
21 |
20
|
r19.29an |
|
22 |
|
simpll |
|
23 |
|
eqid |
|
24 |
23
|
subginvcl |
|
25 |
24
|
adantr |
|
26 |
|
simpr |
|
27 |
9
|
subgcl |
|
28 |
22 25 26 27
|
syl3anc |
|
29 |
|
oveq2 |
|
30 |
29
|
eqeq2d |
|
31 |
30
|
adantl |
|
32 |
3
|
adantr |
|
33 |
6
|
adantr |
|
34 |
8
|
sselda |
|
35 |
4 9 23
|
grpasscan1 |
|
36 |
32 33 34 35
|
syl3anc |
|
37 |
36
|
eqcomd |
|
38 |
28 31 37
|
rspcedvd |
|
39 |
21 38
|
impbida |
|
40 |
11 16 39
|
3bitrd |
|
41 |
40
|
eqrdv |
|