Step |
Hyp |
Ref |
Expression |
1 |
|
ghmgrp.f |
|
2 |
|
ghmgrp.x |
|
3 |
|
ghmgrp.y |
|
4 |
|
ghmgrp.p |
|
5 |
|
ghmgrp.q |
|
6 |
|
ghmgrp.1 |
|
7 |
|
ghmgrp.3 |
|
8 |
|
grpmnd |
|
9 |
7 8
|
syl |
|
10 |
1 2 3 4 5 6 9
|
mhmmnd |
|
11 |
|
fof |
|
12 |
6 11
|
syl |
|
13 |
12
|
ad3antrrr |
|
14 |
7
|
ad3antrrr |
|
15 |
|
simplr |
|
16 |
|
eqid |
|
17 |
2 16
|
grpinvcl |
|
18 |
14 15 17
|
syl2anc |
|
19 |
13 18
|
ffvelrnd |
|
20 |
1
|
3adant1r |
|
21 |
7 17
|
sylan |
|
22 |
|
simpr |
|
23 |
20 21 22
|
mhmlem |
|
24 |
23
|
ad4ant13 |
|
25 |
|
eqid |
|
26 |
2 4 25 16
|
grplinv |
|
27 |
26
|
fveq2d |
|
28 |
14 15 27
|
syl2anc |
|
29 |
1 2 3 4 5 6 9 25
|
mhmid |
|
30 |
29
|
ad3antrrr |
|
31 |
28 30
|
eqtrd |
|
32 |
|
simpr |
|
33 |
32
|
oveq2d |
|
34 |
24 31 33
|
3eqtr3rd |
|
35 |
|
oveq1 |
|
36 |
35
|
eqeq1d |
|
37 |
36
|
rspcev |
|
38 |
19 34 37
|
syl2anc |
|
39 |
|
foelrni |
|
40 |
6 39
|
sylan |
|
41 |
38 40
|
r19.29a |
|
42 |
41
|
ralrimiva |
|
43 |
|
eqid |
|
44 |
3 5 43
|
isgrp |
|
45 |
10 42 44
|
sylanbrc |
|