Step |
Hyp |
Ref |
Expression |
1 |
|
ghmgrp.f |
|
2 |
|
ghmgrp.x |
|
3 |
|
ghmgrp.y |
|
4 |
|
ghmgrp.p |
|
5 |
|
ghmgrp.q |
|
6 |
|
ghmgrp.1 |
|
7 |
|
mhmmnd.3 |
|
8 |
|
mhmid.0 |
|
9 |
|
eqid |
|
10 |
|
fof |
|
11 |
6 10
|
syl |
|
12 |
2 8
|
mndidcl |
|
13 |
7 12
|
syl |
|
14 |
11 13
|
ffvelrnd |
|
15 |
|
simplll |
|
16 |
15 1
|
syl3an1 |
|
17 |
7
|
ad3antrrr |
|
18 |
17 12
|
syl |
|
19 |
|
simplr |
|
20 |
16 18 19
|
mhmlem |
|
21 |
2 4 8
|
mndlid |
|
22 |
17 19 21
|
syl2anc |
|
23 |
22
|
fveq2d |
|
24 |
20 23
|
eqtr3d |
|
25 |
|
simpr |
|
26 |
25
|
oveq2d |
|
27 |
24 26 25
|
3eqtr3d |
|
28 |
|
foelrni |
|
29 |
6 28
|
sylan |
|
30 |
27 29
|
r19.29a |
|
31 |
16 19 18
|
mhmlem |
|
32 |
2 4 8
|
mndrid |
|
33 |
17 19 32
|
syl2anc |
|
34 |
33
|
fveq2d |
|
35 |
31 34
|
eqtr3d |
|
36 |
25
|
oveq1d |
|
37 |
35 36 25
|
3eqtr3d |
|
38 |
37 29
|
r19.29a |
|
39 |
3 9 5 14 30 38
|
ismgmid2 |
|