Step |
Hyp |
Ref |
Expression |
1 |
|
elnmz.1 |
|
2 |
|
nmzsubg.2 |
|
3 |
|
nmzsubg.3 |
|
4 |
2
|
subgss |
|
5 |
4
|
sselda |
|
6 |
|
simpll |
|
7 |
|
subgrcl |
|
8 |
6 7
|
syl |
|
9 |
6 4
|
syl |
|
10 |
|
simplrl |
|
11 |
9 10
|
sseldd |
|
12 |
|
eqid |
|
13 |
|
eqid |
|
14 |
2 3 12 13
|
grplinv |
|
15 |
8 11 14
|
syl2anc |
|
16 |
15
|
oveq1d |
|
17 |
13
|
subginvcl |
|
18 |
6 10 17
|
syl2anc |
|
19 |
9 18
|
sseldd |
|
20 |
|
simplrr |
|
21 |
2 3
|
grpass |
|
22 |
8 19 11 20 21
|
syl13anc |
|
23 |
2 3 12
|
grplid |
|
24 |
8 20 23
|
syl2anc |
|
25 |
16 22 24
|
3eqtr3d |
|
26 |
|
simpr |
|
27 |
3
|
subgcl |
|
28 |
6 18 26 27
|
syl3anc |
|
29 |
25 28
|
eqeltrrd |
|
30 |
3
|
subgcl |
|
31 |
6 29 10 30
|
syl3anc |
|
32 |
|
simpll |
|
33 |
|
simplrl |
|
34 |
32 7
|
syl |
|
35 |
|
simplrr |
|
36 |
32 33 5
|
syl2anc |
|
37 |
|
eqid |
|
38 |
2 3 37
|
grppncan |
|
39 |
34 35 36 38
|
syl3anc |
|
40 |
|
simpr |
|
41 |
37
|
subgsubcl |
|
42 |
32 40 33 41
|
syl3anc |
|
43 |
39 42
|
eqeltrrd |
|
44 |
3
|
subgcl |
|
45 |
32 33 43 44
|
syl3anc |
|
46 |
31 45
|
impbida |
|
47 |
46
|
anassrs |
|
48 |
47
|
ralrimiva |
|
49 |
1
|
elnmz |
|
50 |
5 48 49
|
sylanbrc |
|
51 |
50
|
ex |
|
52 |
51
|
ssrdv |
|