Step |
Hyp |
Ref |
Expression |
1 |
|
ghmgrp.f |
|
2 |
|
mhmlem.a |
|
3 |
|
mhmlem.b |
|
4 |
|
id |
|
5 |
|
eleq1 |
|
6 |
5
|
3anbi2d |
|
7 |
|
fvoveq1 |
|
8 |
|
fveq2 |
|
9 |
8
|
oveq1d |
|
10 |
7 9
|
eqeq12d |
|
11 |
6 10
|
imbi12d |
|
12 |
|
eleq1 |
|
13 |
12
|
3anbi3d |
|
14 |
|
oveq2 |
|
15 |
14
|
fveq2d |
|
16 |
|
fveq2 |
|
17 |
16
|
oveq2d |
|
18 |
15 17
|
eqeq12d |
|
19 |
13 18
|
imbi12d |
|
20 |
11 19 1
|
vtocl2g |
|
21 |
2 3 20
|
syl2anc |
|
22 |
4 2 3 21
|
mp3and |
|