Step |
Hyp |
Ref |
Expression |
1 |
|
dfgrp2.b |
|
2 |
|
dfgrp2.p |
|
3 |
|
grpsgrp |
|
4 |
|
grpmnd |
|
5 |
|
eqid |
|
6 |
1 5
|
mndidcl |
|
7 |
4 6
|
syl |
|
8 |
|
oveq1 |
|
9 |
8
|
eqeq1d |
|
10 |
|
eqeq2 |
|
11 |
10
|
rexbidv |
|
12 |
9 11
|
anbi12d |
|
13 |
12
|
ralbidv |
|
14 |
13
|
adantl |
|
15 |
1 2 5
|
mndlid |
|
16 |
4 15
|
sylan |
|
17 |
1 2 5
|
grpinvex |
|
18 |
16 17
|
jca |
|
19 |
18
|
ralrimiva |
|
20 |
7 14 19
|
rspcedvd |
|
21 |
3 20
|
jca |
|
22 |
1
|
a1i |
|
23 |
2
|
a1i |
|
24 |
|
sgrpmgm |
|
25 |
24
|
adantl |
|
26 |
1 2
|
mgmcl |
|
27 |
25 26
|
syl3an1 |
|
28 |
1 2
|
sgrpass |
|
29 |
28
|
adantll |
|
30 |
|
simpll |
|
31 |
|
oveq2 |
|
32 |
|
id |
|
33 |
31 32
|
eqeq12d |
|
34 |
|
oveq2 |
|
35 |
34
|
eqeq1d |
|
36 |
35
|
rexbidv |
|
37 |
33 36
|
anbi12d |
|
38 |
37
|
rspcv |
|
39 |
|
simpl |
|
40 |
38 39
|
syl6com |
|
41 |
40
|
ad2antlr |
|
42 |
41
|
imp |
|
43 |
|
oveq1 |
|
44 |
43
|
eqeq1d |
|
45 |
44
|
cbvrexvw |
|
46 |
45
|
biimpi |
|
47 |
46
|
adantl |
|
48 |
38 47
|
syl6com |
|
49 |
48
|
ad2antlr |
|
50 |
49
|
imp |
|
51 |
22 23 27 29 30 42 50
|
isgrpde |
|
52 |
51
|
ex |
|
53 |
52
|
rexlimiva |
|
54 |
53
|
impcom |
|
55 |
21 54
|
impbii |
|