Step | Hyp | Ref
| Expression |
1 | | gaset 17726 |
. . 3
|
2 | | gasubg.1 |
. . . 4
↾s |
3 | 2 | subggrp 17597 |
. . 3
SubGrp
|
4 | 1, 3 | anim12ci 591 |
. 2
SubGrp
|
5 | | eqid 2622 |
. . . . . . 7
|
6 | 5 | gaf 17728 |
. . . . . 6
|
7 | 6 | adantr 481 |
. . . . 5
SubGrp
|
8 | | simpr 477 |
. . . . . . 7
SubGrp
SubGrp |
9 | 5 | subgss 17595 |
. . . . . . 7
SubGrp
|
10 | 8, 9 | syl 17 |
. . . . . 6
SubGrp
|
11 | | xpss1 5228 |
. . . . . 6
|
12 | 10, 11 | syl 17 |
. . . . 5
SubGrp
|
13 | 7, 12 | fssresd 6071 |
. . . 4
SubGrp
|
14 | 2 | subgbas 17598 |
. . . . . . 7
SubGrp
|
15 | 8, 14 | syl 17 |
. . . . . 6
SubGrp
|
16 | 15 | xpeq1d 5138 |
. . . . 5
SubGrp
|
17 | 16 | feq2d 6031 |
. . . 4
SubGrp
|
18 | 13, 17 | mpbid 222 |
. . 3
SubGrp
|
19 | 8 | adantr 481 |
. . . . . . . 8
SubGrp SubGrp |
20 | | eqid 2622 |
. . . . . . . . 9
|
21 | 20 | subg0cl 17602 |
. . . . . . . 8
SubGrp
|
22 | 19, 21 | syl 17 |
. . . . . . 7
SubGrp |
23 | | simpr 477 |
. . . . . . 7
SubGrp |
24 | | ovres 6800 |
. . . . . . 7
|
25 | 22, 23, 24 | syl2anc 693 |
. . . . . 6
SubGrp |
26 | 2, 20 | subg0 17600 |
. . . . . . . 8
SubGrp
|
27 | 19, 26 | syl 17 |
. . . . . . 7
SubGrp |
28 | 27 | oveq1d 6665 |
. . . . . 6
SubGrp |
29 | 20 | gagrpid 17727 |
. . . . . . 7
|
30 | 29 | adantlr 751 |
. . . . . 6
SubGrp |
31 | 25, 28, 30 | 3eqtr3d 2664 |
. . . . 5
SubGrp |
32 | | eqimss2 3658 |
. . . . . . . . . . 11
|
33 | 15, 32 | syl 17 |
. . . . . . . . . 10
SubGrp
|
34 | 33 | adantr 481 |
. . . . . . . . 9
SubGrp |
35 | 34 | sselda 3603 |
. . . . . . . 8
SubGrp |
36 | 34 | sselda 3603 |
. . . . . . . 8
SubGrp |
37 | 35, 36 | anim12dan 882 |
. . . . . . 7
SubGrp
|
38 | | simprl 794 |
. . . . . . . . . 10
SubGrp
|
39 | 7 | ad2antrr 762 |
. . . . . . . . . . 11
SubGrp
|
40 | 9 | ad3antlr 767 |
. . . . . . . . . . . 12
SubGrp
|
41 | | simprr 796 |
. . . . . . . . . . . 12
SubGrp
|
42 | 40, 41 | sseldd 3604 |
. . . . . . . . . . 11
SubGrp
|
43 | 23 | adantr 481 |
. . . . . . . . . . 11
SubGrp
|
44 | 39, 42, 43 | fovrnd 6806 |
. . . . . . . . . 10
SubGrp
|
45 | | ovres 6800 |
. . . . . . . . . 10
|
46 | 38, 44, 45 | syl2anc 693 |
. . . . . . . . 9
SubGrp
|
47 | | ovres 6800 |
. . . . . . . . . . 11
|
48 | 41, 43, 47 | syl2anc 693 |
. . . . . . . . . 10
SubGrp
|
49 | 48 | oveq2d 6666 |
. . . . . . . . 9
SubGrp
|
50 | | simplll 798 |
. . . . . . . . . 10
SubGrp
|
51 | 40, 38 | sseldd 3604 |
. . . . . . . . . 10
SubGrp
|
52 | | eqid 2622 |
. . . . . . . . . . 11
|
53 | 5, 52 | gaass 17730 |
. . . . . . . . . 10
|
54 | 50, 51, 42, 43, 53 | syl13anc 1328 |
. . . . . . . . 9
SubGrp
|
55 | 46, 49, 54 | 3eqtr4d 2666 |
. . . . . . . 8
SubGrp
|
56 | 52 | subgcl 17604 |
. . . . . . . . . . 11
SubGrp
|
57 | 56 | 3expb 1266 |
. . . . . . . . . 10
SubGrp
|
58 | 19, 57 | sylan 488 |
. . . . . . . . 9
SubGrp
|
59 | | ovres 6800 |
. . . . . . . . 9
|
60 | 58, 43, 59 | syl2anc 693 |
. . . . . . . 8
SubGrp
|
61 | 2, 52 | ressplusg 15993 |
. . . . . . . . . . 11
SubGrp
|
62 | 61 | ad3antlr 767 |
. . . . . . . . . 10
SubGrp
|
63 | 62 | oveqd 6667 |
. . . . . . . . 9
SubGrp
|
64 | 63 | oveq1d 6665 |
. . . . . . . 8
SubGrp
|
65 | 55, 60, 64 | 3eqtr2rd 2663 |
. . . . . . 7
SubGrp
|
66 | 37, 65 | syldan 487 |
. . . . . 6
SubGrp |
67 | 66 | ralrimivva 2971 |
. . . . 5
SubGrp
|
68 | 31, 67 | jca 554 |
. . . 4
SubGrp
|
69 | 68 | ralrimiva 2966 |
. . 3
SubGrp
|
70 | 18, 69 | jca 554 |
. 2
SubGrp
|
71 | | eqid 2622 |
. . 3
|
72 | | eqid 2622 |
. . 3
|
73 | | eqid 2622 |
. . 3
|
74 | 71, 72, 73 | isga 17724 |
. 2
|
75 | 4, 70, 74 | sylanbrc 698 |
1
SubGrp
|