Step |
Hyp |
Ref |
Expression |
1 |
|
ascldimul.a |
|
2 |
|
ascldimul.f |
|
3 |
|
ascldimul.k |
|
4 |
|
ascldimul.t |
|
5 |
|
ascldimul.s |
|
6 |
|
assaring |
|
7 |
|
eqid |
|
8 |
|
eqid |
|
9 |
7 8
|
ringidcl |
|
10 |
6 9
|
syl |
|
11 |
7 4 8
|
ringlidm |
|
12 |
6 10 11
|
syl2anc |
|
13 |
12
|
oveq2d |
|
14 |
13
|
oveq2d |
|
15 |
14
|
3ad2ant1 |
|
16 |
|
simp1 |
|
17 |
|
simp2 |
|
18 |
10
|
3ad2ant1 |
|
19 |
|
assalmod |
|
20 |
19
|
3ad2ant1 |
|
21 |
|
simp3 |
|
22 |
|
eqid |
|
23 |
7 2 22 3
|
lmodvscl |
|
24 |
20 21 18 23
|
syl3anc |
|
25 |
7 2 3 22 4
|
assaass |
|
26 |
16 17 18 24 25
|
syl13anc |
|
27 |
7 2 3 22 4
|
assaassr |
|
28 |
16 21 18 18 27
|
syl13anc |
|
29 |
28
|
oveq2d |
|
30 |
26 29
|
eqtrd |
|
31 |
7 2 22 3 5
|
lmodvsass |
|
32 |
20 17 21 18 31
|
syl13anc |
|
33 |
15 30 32
|
3eqtr4rd |
|
34 |
2
|
assasca |
|
35 |
|
crngring |
|
36 |
34 35
|
syl |
|
37 |
3 5
|
ringcl |
|
38 |
36 37
|
syl3an1 |
|
39 |
1 2 3 22 8
|
asclval |
|
40 |
38 39
|
syl |
|
41 |
1 2 3 22 8
|
asclval |
|
42 |
17 41
|
syl |
|
43 |
1 2 3 22 8
|
asclval |
|
44 |
21 43
|
syl |
|
45 |
42 44
|
oveq12d |
|
46 |
33 40 45
|
3eqtr4d |
|