Step |
Hyp |
Ref |
Expression |
1 |
|
subgdprd.1 |
|
2 |
|
subgdprd.2 |
|
3 |
|
subgdprd.3 |
|
4 |
|
subgdprd.4 |
|
5 |
1
|
subggrp |
|
6 |
2 5
|
syl |
|
7 |
|
eqid |
|
8 |
7
|
subgacs |
|
9 |
|
acsmre |
|
10 |
6 8 9
|
3syl |
|
11 |
|
subgrcl |
|
12 |
2 11
|
syl |
|
13 |
|
eqid |
|
14 |
13
|
subgacs |
|
15 |
|
acsmre |
|
16 |
12 14 15
|
3syl |
|
17 |
|
eqid |
|
18 |
|
dprdf |
|
19 |
|
frn |
|
20 |
3 18 19
|
3syl |
|
21 |
|
mresspw |
|
22 |
16 21
|
syl |
|
23 |
20 22
|
sstrd |
|
24 |
|
sspwuni |
|
25 |
23 24
|
sylib |
|
26 |
16 17 25
|
mrcssidd |
|
27 |
17
|
mrccl |
|
28 |
16 25 27
|
syl2anc |
|
29 |
|
sspwuni |
|
30 |
4 29
|
sylib |
|
31 |
17
|
mrcsscl |
|
32 |
16 30 2 31
|
syl3anc |
|
33 |
1
|
subsubg |
|
34 |
2 33
|
syl |
|
35 |
28 32 34
|
mpbir2and |
|
36 |
|
eqid |
|
37 |
36
|
mrcsscl |
|
38 |
10 26 35 37
|
syl3anc |
|
39 |
1
|
subgdmdprd |
|
40 |
2 39
|
syl |
|
41 |
3 4 40
|
mpbir2and |
|
42 |
|
eqidd |
|
43 |
41 42
|
dprdf2 |
|
44 |
43
|
frnd |
|
45 |
|
mresspw |
|
46 |
10 45
|
syl |
|
47 |
44 46
|
sstrd |
|
48 |
|
sspwuni |
|
49 |
47 48
|
sylib |
|
50 |
10 36 49
|
mrcssidd |
|
51 |
36
|
mrccl |
|
52 |
10 49 51
|
syl2anc |
|
53 |
1
|
subsubg |
|
54 |
2 53
|
syl |
|
55 |
52 54
|
mpbid |
|
56 |
55
|
simpld |
|
57 |
17
|
mrcsscl |
|
58 |
16 50 56 57
|
syl3anc |
|
59 |
38 58
|
eqssd |
|
60 |
36
|
dprdspan |
|
61 |
41 60
|
syl |
|
62 |
17
|
dprdspan |
|
63 |
3 62
|
syl |
|
64 |
59 61 63
|
3eqtr4d |
|