Step |
Hyp |
Ref |
Expression |
1 |
|
mplmon2cl.p |
|
2 |
|
mplmon2cl.d |
|
3 |
|
mplmon2cl.z |
|
4 |
|
mplmon2cl.c |
|
5 |
|
mplmon2cl.i |
|
6 |
|
mplmon2mul.r |
|
7 |
|
mplmon2mul.t |
|
8 |
|
mplmon2mul.u |
|
9 |
|
mplmon2mul.x |
|
10 |
|
mplmon2mul.y |
|
11 |
|
mplmon2mul.f |
|
12 |
|
mplmon2mul.g |
|
13 |
1
|
mplassa |
|
14 |
5 6 13
|
syl2anc |
|
15 |
1 5 6
|
mplsca |
|
16 |
15
|
fveq2d |
|
17 |
4 16
|
syl5eq |
|
18 |
11 17
|
eleqtrd |
|
19 |
|
eqid |
|
20 |
|
eqid |
|
21 |
|
crngring |
|
22 |
6 21
|
syl |
|
23 |
1 19 3 20 2 5 22 9
|
mplmon |
|
24 |
|
assalmod |
|
25 |
14 24
|
syl |
|
26 |
12 17
|
eleqtrd |
|
27 |
1 19 3 20 2 5 22 10
|
mplmon |
|
28 |
|
eqid |
|
29 |
|
eqid |
|
30 |
|
eqid |
|
31 |
19 28 29 30
|
lmodvscl |
|
32 |
25 26 27 31
|
syl3anc |
|
33 |
19 28 30 29 7
|
assaass |
|
34 |
14 18 23 32 33
|
syl13anc |
|
35 |
19 28 30 29 7
|
assaassr |
|
36 |
14 26 23 27 35
|
syl13anc |
|
37 |
36
|
oveq2d |
|
38 |
1 19 3 20 2 5 22 9 7 10
|
mplmonmul |
|
39 |
38
|
oveq2d |
|
40 |
39
|
oveq2d |
|
41 |
2
|
psrbagaddcl |
|
42 |
9 10 41
|
syl2anc |
|
43 |
1 19 3 20 2 5 22 42
|
mplmon |
|
44 |
|
eqid |
|
45 |
19 28 29 30 44
|
lmodvsass |
|
46 |
25 18 26 43 45
|
syl13anc |
|
47 |
15
|
fveq2d |
|
48 |
8 47
|
syl5req |
|
49 |
48
|
oveqd |
|
50 |
49
|
oveq1d |
|
51 |
40 46 50
|
3eqtr2d |
|
52 |
34 37 51
|
3eqtrd |
|
53 |
1 29 2 20 3 4 5 22 9 11
|
mplmon2 |
|
54 |
1 29 2 20 3 4 5 22 10 12
|
mplmon2 |
|
55 |
53 54
|
oveq12d |
|
56 |
4 8
|
ringcl |
|
57 |
22 11 12 56
|
syl3anc |
|
58 |
1 29 2 20 3 4 5 22 42 57
|
mplmon2 |
|
59 |
52 55 58
|
3eqtr3d |
|