Step |
Hyp |
Ref |
Expression |
1 |
|
resmgmhm.u |
|
2 |
|
mgmhmrcl |
|
3 |
2
|
simprd |
|
4 |
1
|
submgmmgm |
|
5 |
3 4
|
anim12ci |
|
6 |
|
eqid |
|
7 |
|
eqid |
|
8 |
6 7
|
mgmhmf |
|
9 |
6
|
submgmss |
|
10 |
|
fssres |
|
11 |
8 9 10
|
syl2an |
|
12 |
9
|
adantl |
|
13 |
1 6
|
ressbas2 |
|
14 |
12 13
|
syl |
|
15 |
14
|
feq2d |
|
16 |
11 15
|
mpbid |
|
17 |
|
simpll |
|
18 |
9
|
ad2antlr |
|
19 |
|
simprl |
|
20 |
18 19
|
sseldd |
|
21 |
|
simprr |
|
22 |
18 21
|
sseldd |
|
23 |
|
eqid |
|
24 |
|
eqid |
|
25 |
6 23 24
|
mgmhmlin |
|
26 |
17 20 22 25
|
syl3anc |
|
27 |
23
|
submgmcl |
|
28 |
27
|
3expb |
|
29 |
28
|
adantll |
|
30 |
|
fvres |
|
31 |
29 30
|
syl |
|
32 |
|
fvres |
|
33 |
|
fvres |
|
34 |
32 33
|
oveqan12d |
|
35 |
34
|
adantl |
|
36 |
26 31 35
|
3eqtr4d |
|
37 |
36
|
ralrimivva |
|
38 |
1 23
|
ressplusg |
|
39 |
38
|
adantl |
|
40 |
39
|
oveqd |
|
41 |
40
|
fveqeq2d |
|
42 |
14 41
|
raleqbidv |
|
43 |
14 42
|
raleqbidv |
|
44 |
37 43
|
mpbid |
|
45 |
16 44
|
jca |
|
46 |
|
eqid |
|
47 |
|
eqid |
|
48 |
46 7 47 24
|
ismgmhm |
|
49 |
5 45 48
|
sylanbrc |
|