Step |
Hyp |
Ref |
Expression |
1 |
|
ghmmhm |
|
2 |
|
ghmmhm |
|
3 |
|
mhmeql |
|
4 |
1 2 3
|
syl2an |
|
5 |
|
fveq2 |
|
6 |
|
fveq2 |
|
7 |
5 6
|
eqeq12d |
|
8 |
|
ghmgrp1 |
|
9 |
8
|
adantr |
|
10 |
9
|
adantr |
|
11 |
|
simprl |
|
12 |
|
eqid |
|
13 |
|
eqid |
|
14 |
12 13
|
grpinvcl |
|
15 |
10 11 14
|
syl2anc |
|
16 |
|
simprr |
|
17 |
16
|
fveq2d |
|
18 |
|
eqid |
|
19 |
12 13 18
|
ghminv |
|
20 |
19
|
ad2ant2r |
|
21 |
12 13 18
|
ghminv |
|
22 |
21
|
ad2ant2lr |
|
23 |
17 20 22
|
3eqtr4d |
|
24 |
7 15 23
|
elrabd |
|
25 |
24
|
expr |
|
26 |
25
|
ralrimiva |
|
27 |
|
fveq2 |
|
28 |
|
fveq2 |
|
29 |
27 28
|
eqeq12d |
|
30 |
29
|
ralrab |
|
31 |
26 30
|
sylibr |
|
32 |
|
eqid |
|
33 |
12 32
|
ghmf |
|
34 |
33
|
adantr |
|
35 |
34
|
ffnd |
|
36 |
12 32
|
ghmf |
|
37 |
36
|
adantl |
|
38 |
37
|
ffnd |
|
39 |
|
fndmin |
|
40 |
35 38 39
|
syl2anc |
|
41 |
|
eleq2 |
|
42 |
41
|
raleqbi1dv |
|
43 |
40 42
|
syl |
|
44 |
31 43
|
mpbird |
|
45 |
13
|
issubg3 |
|
46 |
9 45
|
syl |
|
47 |
4 44 46
|
mpbir2and |
|