Step |
Hyp |
Ref |
Expression |
1 |
|
grpissubg.b |
|
2 |
|
grpissubg.s |
|
3 |
|
simpl |
|
4 |
3
|
adantl |
|
5 |
2
|
grpbn0 |
|
6 |
5
|
ad2antlr |
|
7 |
|
grpmnd |
|
8 |
|
mndmgm |
|
9 |
7 8
|
syl |
|
10 |
|
grpmnd |
|
11 |
|
mndmgm |
|
12 |
10 11
|
syl |
|
13 |
9 12
|
anim12i |
|
14 |
13
|
adantr |
|
15 |
14
|
ad2antrr |
|
16 |
|
simpr |
|
17 |
16
|
ad2antrr |
|
18 |
|
simpr |
|
19 |
18
|
anim1i |
|
20 |
1 2
|
mgmsscl |
|
21 |
15 17 19 20
|
syl3anc |
|
22 |
21
|
ralrimiva |
|
23 |
|
simpl |
|
24 |
23
|
adantr |
|
25 |
|
simplr |
|
26 |
1
|
sseq2i |
|
27 |
26
|
biimpi |
|
28 |
27
|
adantr |
|
29 |
28
|
adantl |
|
30 |
|
ovres |
|
31 |
30
|
adantl |
|
32 |
|
oveq |
|
33 |
32
|
adantl |
|
34 |
33
|
eqcomd |
|
35 |
34
|
ad2antlr |
|
36 |
31 35
|
eqtr3d |
|
37 |
36
|
ralrimivva |
|
38 |
24 25 2 29 37
|
grpinvssd |
|
39 |
38
|
imp |
|
40 |
|
eqid |
|
41 |
2 40
|
grpinvcl |
|
42 |
41
|
ad4ant24 |
|
43 |
39 42
|
eqeltrrd |
|
44 |
22 43
|
jca |
|
45 |
44
|
ralrimiva |
|
46 |
|
eqid |
|
47 |
|
eqid |
|
48 |
1 46 47
|
issubg2 |
|
49 |
48
|
ad2antrr |
|
50 |
4 6 45 49
|
mpbir3and |
|
51 |
50
|
ex |
|