Step |
Hyp |
Ref |
Expression |
1 |
|
monmat2matmon.p |
|
2 |
|
monmat2matmon.c |
|
3 |
|
monmat2matmon.b |
|
4 |
|
monmat2matmon.m1 |
|
5 |
|
monmat2matmon.e1 |
|
6 |
|
monmat2matmon.x |
|
7 |
|
monmat2matmon.a |
|
8 |
|
monmat2matmon.k |
|
9 |
|
monmat2matmon.q |
|
10 |
|
monmat2matmon.i |
|
11 |
|
monmat2matmon.e2 |
|
12 |
|
monmat2matmon.y |
|
13 |
|
monmat2matmon.m2 |
|
14 |
|
monmat2matmon.t |
|
15 |
|
crngring |
|
16 |
|
simpll |
|
17 |
|
simplr |
|
18 |
7 8 14 1 2 3 13 11 12
|
mat2pmatscmxcl |
|
19 |
1 2 3 4 5 6 7 9 10
|
pm2mpfval |
|
20 |
16 17 18 19
|
syl3anc |
|
21 |
15 20
|
sylanl2 |
|
22 |
|
simpll |
|
23 |
|
simpr |
|
24 |
23
|
anim1i |
|
25 |
|
df-3an |
|
26 |
24 25
|
sylibr |
|
27 |
|
eqid |
|
28 |
1 2 7 8 27 11 12 13 14
|
monmatcollpw |
|
29 |
22 26 28
|
syl2anc |
|
30 |
29
|
oveq1d |
|
31 |
15
|
a1i |
|
32 |
31
|
anim2d |
|
33 |
32
|
anim1d |
|
34 |
33
|
imdistanri |
|
35 |
|
ovif |
|
36 |
7
|
matring |
|
37 |
9
|
ply1sca |
|
38 |
36 37
|
syl |
|
39 |
38
|
ad2antrr |
|
40 |
39
|
fveq2d |
|
41 |
40
|
oveq1d |
|
42 |
9
|
ply1lmod |
|
43 |
36 42
|
syl |
|
44 |
43
|
ad2antrr |
|
45 |
|
eqid |
|
46 |
|
eqid |
|
47 |
45 46
|
mgpbas |
|
48 |
9
|
ply1ring |
|
49 |
36 48
|
syl |
|
50 |
45
|
ringmgp |
|
51 |
49 50
|
syl |
|
52 |
51
|
ad2antrr |
|
53 |
|
simpr |
|
54 |
6 9 46
|
vr1cl |
|
55 |
36 54
|
syl |
|
56 |
55
|
ad2antrr |
|
57 |
47 5 52 53 56
|
mulgnn0cld |
|
58 |
|
eqid |
|
59 |
|
eqid |
|
60 |
|
eqid |
|
61 |
46 58 4 59 60
|
lmod0vs |
|
62 |
44 57 61
|
syl2anc |
|
63 |
41 62
|
eqtrd |
|
64 |
63
|
ifeq2d |
|
65 |
35 64
|
eqtrid |
|
66 |
34 65
|
syl |
|
67 |
30 66
|
eqtrd |
|
68 |
67
|
mpteq2dva |
|
69 |
68
|
oveq2d |
|
70 |
|
ringmnd |
|
71 |
49 70
|
syl |
|
72 |
71
|
adantr |
|
73 |
|
nn0ex |
|
74 |
73
|
a1i |
|
75 |
|
simprr |
|
76 |
|
eqid |
|
77 |
38
|
fveq2d |
|
78 |
8 77
|
eqtrid |
|
79 |
78
|
eleq2d |
|
80 |
79
|
biimpcd |
|
81 |
80
|
adantr |
|
82 |
81
|
impcom |
|
83 |
82
|
adantr |
|
84 |
|
eqid |
|
85 |
46 58 4 84
|
lmodvscl |
|
86 |
44 83 57 85
|
syl3anc |
|
87 |
86
|
ralrimiva |
|
88 |
60 72 74 75 76 87
|
gsummpt1n0 |
|
89 |
15 88
|
sylanl2 |
|
90 |
69 89
|
eqtrd |
|
91 |
|
csbov2g |
|
92 |
|
csbov1g |
|
93 |
|
csbvarg |
|
94 |
93
|
oveq1d |
|
95 |
92 94
|
eqtrd |
|
96 |
95
|
oveq2d |
|
97 |
91 96
|
eqtrd |
|
98 |
97
|
ad2antll |
|
99 |
21 90 98
|
3eqtrd |
|