Step |
Hyp |
Ref |
Expression |
1 |
|
dsmmsubg.p |
|
2 |
|
dsmmsubg.h |
|
3 |
|
dsmmsubg.i |
|
4 |
|
dsmmsubg.s |
|
5 |
|
dsmmsubg.r |
|
6 |
|
eqidd |
|
7 |
|
eqidd |
|
8 |
|
eqidd |
|
9 |
|
fex |
|
10 |
5 3 9
|
syl2anc |
|
11 |
|
eqid |
|
12 |
11
|
dsmmbase |
|
13 |
10 12
|
syl |
|
14 |
|
ssrab2 |
|
15 |
13 14
|
eqsstrrdi |
|
16 |
1
|
fveq2i |
|
17 |
15 2 16
|
3sstr4g |
|
18 |
|
grpmnd |
|
19 |
18
|
ssriv |
|
20 |
|
fss |
|
21 |
5 19 20
|
sylancl |
|
22 |
|
eqid |
|
23 |
1 2 3 4 21 22
|
dsmm0cl |
|
24 |
3
|
3ad2ant1 |
|
25 |
4
|
3ad2ant1 |
|
26 |
21
|
3ad2ant1 |
|
27 |
|
simp2 |
|
28 |
|
simp3 |
|
29 |
|
eqid |
|
30 |
1 2 24 25 26 27 28 29
|
dsmmacl |
|
31 |
1 3 4 5
|
prdsgrpd |
|
32 |
31
|
adantr |
|
33 |
17
|
sselda |
|
34 |
|
eqid |
|
35 |
|
eqid |
|
36 |
34 35
|
grpinvcl |
|
37 |
32 33 36
|
syl2anc |
|
38 |
|
simpr |
|
39 |
|
eqid |
|
40 |
3
|
adantr |
|
41 |
5
|
ffnd |
|
42 |
41
|
adantr |
|
43 |
1 39 34 2 40 42
|
dsmmelbas |
|
44 |
38 43
|
mpbid |
|
45 |
44
|
simprd |
|
46 |
3
|
ad2antrr |
|
47 |
4
|
ad2antrr |
|
48 |
5
|
ad2antrr |
|
49 |
33
|
adantr |
|
50 |
|
simpr |
|
51 |
1 46 47 48 34 35 49 50
|
prdsinvgd2 |
|
52 |
51
|
adantrr |
|
53 |
|
fveq2 |
|
54 |
53
|
ad2antll |
|
55 |
5
|
ffvelrnda |
|
56 |
55
|
adantlr |
|
57 |
|
eqid |
|
58 |
|
eqid |
|
59 |
57 58
|
grpinvid |
|
60 |
56 59
|
syl |
|
61 |
60
|
adantrr |
|
62 |
52 54 61
|
3eqtrd |
|
63 |
62
|
expr |
|
64 |
63
|
necon3d |
|
65 |
64
|
ss2rabdv |
|
66 |
45 65
|
ssfid |
|
67 |
1 39 34 2 40 42
|
dsmmelbas |
|
68 |
37 66 67
|
mpbir2and |
|
69 |
6 7 8 17 23 30 68 31
|
issubgrpd2 |
|