Step |
Hyp |
Ref |
Expression |
1 |
|
isnsg3.1 |
|
2 |
|
isnsg3.2 |
|
3 |
|
isnsg3.3 |
|
4 |
|
nsgsubg |
|
5 |
1 2 3
|
nsgconj |
|
6 |
5
|
3expb |
|
7 |
6
|
ralrimivva |
|
8 |
4 7
|
jca |
|
9 |
|
simpl |
|
10 |
|
subgrcl |
|
11 |
10
|
ad2antrr |
|
12 |
|
simprll |
|
13 |
|
eqid |
|
14 |
|
eqid |
|
15 |
1 2 13 14
|
grplinv |
|
16 |
11 12 15
|
syl2anc |
|
17 |
16
|
oveq1d |
|
18 |
1 14
|
grpinvcl |
|
19 |
11 12 18
|
syl2anc |
|
20 |
|
simprlr |
|
21 |
1 2
|
grpass |
|
22 |
11 19 12 20 21
|
syl13anc |
|
23 |
1 2 13
|
grplid |
|
24 |
11 20 23
|
syl2anc |
|
25 |
17 22 24
|
3eqtr3d |
|
26 |
25
|
oveq1d |
|
27 |
1 2 3 14 11 20 12
|
grpsubinv |
|
28 |
26 27
|
eqtrd |
|
29 |
|
simprr |
|
30 |
|
simplr |
|
31 |
|
oveq1 |
|
32 |
|
id |
|
33 |
31 32
|
oveq12d |
|
34 |
33
|
eleq1d |
|
35 |
|
oveq2 |
|
36 |
35
|
oveq1d |
|
37 |
36
|
eleq1d |
|
38 |
34 37
|
rspc2va |
|
39 |
19 29 30 38
|
syl21anc |
|
40 |
28 39
|
eqeltrrd |
|
41 |
40
|
expr |
|
42 |
41
|
ralrimivva |
|
43 |
1 2
|
isnsg2 |
|
44 |
9 42 43
|
sylanbrc |
|
45 |
8 44
|
impbii |
|