Step |
Hyp |
Ref |
Expression |
1 |
|
mulgmhm.b |
|
2 |
|
mulgmhm.m |
|
3 |
|
cmnmnd |
|
4 |
3
|
adantr |
|
5 |
1 2
|
mulgnn0cl |
|
6 |
3 5
|
syl3an1 |
|
7 |
6
|
3expa |
|
8 |
7
|
fmpttd |
|
9 |
|
3anass |
|
10 |
|
eqid |
|
11 |
1 2 10
|
mulgnn0di |
|
12 |
9 11
|
sylan2br |
|
13 |
12
|
anassrs |
|
14 |
1 10
|
mndcl |
|
15 |
14
|
3expb |
|
16 |
4 15
|
sylan |
|
17 |
|
oveq2 |
|
18 |
|
eqid |
|
19 |
|
ovex |
|
20 |
17 18 19
|
fvmpt |
|
21 |
16 20
|
syl |
|
22 |
|
oveq2 |
|
23 |
|
ovex |
|
24 |
22 18 23
|
fvmpt |
|
25 |
|
oveq2 |
|
26 |
|
ovex |
|
27 |
25 18 26
|
fvmpt |
|
28 |
24 27
|
oveqan12d |
|
29 |
28
|
adantl |
|
30 |
13 21 29
|
3eqtr4d |
|
31 |
30
|
ralrimivva |
|
32 |
|
eqid |
|
33 |
1 32
|
mndidcl |
|
34 |
|
oveq2 |
|
35 |
|
ovex |
|
36 |
34 18 35
|
fvmpt |
|
37 |
4 33 36
|
3syl |
|
38 |
1 2 32
|
mulgnn0z |
|
39 |
3 38
|
sylan |
|
40 |
37 39
|
eqtrd |
|
41 |
8 31 40
|
3jca |
|
42 |
1 1 10 10 32 32
|
ismhm |
|
43 |
4 4 41 42
|
syl21anbrc |
|