Step |
Hyp |
Ref |
Expression |
1 |
|
resmgmhm2.u |
|
2 |
|
mgmhmrcl |
|
3 |
2
|
simpld |
|
4 |
3
|
adantl |
|
5 |
1
|
submgmmgm |
|
6 |
5
|
ad2antrr |
|
7 |
4 6
|
jca |
|
8 |
|
eqid |
|
9 |
|
eqid |
|
10 |
8 9
|
mgmhmf |
|
11 |
10
|
adantl |
|
12 |
11
|
ffnd |
|
13 |
|
simplr |
|
14 |
|
df-f |
|
15 |
12 13 14
|
sylanbrc |
|
16 |
1
|
submgmbas |
|
17 |
16
|
ad2antrr |
|
18 |
17
|
feq3d |
|
19 |
15 18
|
mpbid |
|
20 |
|
eqid |
|
21 |
|
eqid |
|
22 |
8 20 21
|
mgmhmlin |
|
23 |
22
|
3expb |
|
24 |
23
|
adantll |
|
25 |
1 21
|
ressplusg |
|
26 |
25
|
ad3antrrr |
|
27 |
26
|
oveqd |
|
28 |
24 27
|
eqtrd |
|
29 |
28
|
ralrimivva |
|
30 |
19 29
|
jca |
|
31 |
|
eqid |
|
32 |
|
eqid |
|
33 |
8 31 20 32
|
ismgmhm |
|
34 |
7 30 33
|
sylanbrc |
|
35 |
1
|
resmgmhm2 |
|
36 |
35
|
ancoms |
|
37 |
36
|
adantlr |
|
38 |
34 37
|
impbida |
|