Step |
Hyp |
Ref |
Expression |
1 |
|
pmatcollpwscmat.p |
|
2 |
|
pmatcollpwscmat.c |
|
3 |
|
pmatcollpwscmat.b |
|
4 |
|
pmatcollpwscmat.m1 |
|
5 |
|
pmatcollpwscmat.e1 |
|
6 |
|
pmatcollpwscmat.x |
|
7 |
|
pmatcollpwscmat.t |
|
8 |
|
pmatcollpwscmat.a |
|
9 |
|
pmatcollpwscmat.d |
|
10 |
|
pmatcollpwscmat.u |
|
11 |
|
pmatcollpwscmat.k |
|
12 |
|
pmatcollpwscmat.e2 |
|
13 |
|
pmatcollpwscmat.s |
|
14 |
|
pmatcollpwscmat.1 |
|
15 |
|
pmatcollpwscmat.m2 |
|
16 |
15
|
oveqi |
|
17 |
1
|
ply1ring |
|
18 |
17
|
anim2i |
|
19 |
|
simpr |
|
20 |
18 19
|
anim12i |
|
21 |
|
df-3an |
|
22 |
20 21
|
sylibr |
|
23 |
|
eqid |
|
24 |
2 12 23 14 4
|
scmatscmide |
|
25 |
22 24
|
sylan |
|
26 |
16 25
|
eqtrid |
|
27 |
26
|
fveq2d |
|
28 |
27
|
fveq1d |
|
29 |
|
fvif |
|
30 |
29
|
fveq1i |
|
31 |
|
iffv |
|
32 |
30 31
|
eqtri |
|
33 |
28 32
|
eqtrdi |
|
34 |
33
|
oveq1d |
|
35 |
|
ovif |
|
36 |
|
eqid |
|
37 |
1 23 36
|
coe1z |
|
38 |
37
|
ad2antlr |
|
39 |
38
|
fveq1d |
|
40 |
|
fvexd |
|
41 |
|
simpl |
|
42 |
40 41
|
anim12i |
|
43 |
|
fvconst2g |
|
44 |
42 43
|
syl |
|
45 |
39 44
|
eqtrd |
|
46 |
45
|
oveq1d |
|
47 |
1
|
ply1lmod |
|
48 |
47
|
ad2antlr |
|
49 |
|
eqid |
|
50 |
49 12
|
mgpbas |
|
51 |
|
eqid |
|
52 |
49
|
ringmgp |
|
53 |
17 52
|
syl |
|
54 |
|
0nn0 |
|
55 |
54
|
a1i |
|
56 |
|
eqid |
|
57 |
56 1 12
|
vr1cl |
|
58 |
50 51 53 55 57
|
mulgnn0cld |
|
59 |
58
|
ad2antlr |
|
60 |
|
eqid |
|
61 |
|
eqid |
|
62 |
|
eqid |
|
63 |
12 60 61 62 23
|
lmod0vs |
|
64 |
48 59 63
|
syl2anc |
|
65 |
1
|
ply1sca |
|
66 |
65
|
adantl |
|
67 |
66
|
fveq2d |
|
68 |
67
|
oveq1d |
|
69 |
68
|
eqeq1d |
|
70 |
69
|
adantr |
|
71 |
64 70
|
mpbird |
|
72 |
46 71
|
eqtrd |
|
73 |
72
|
ifeq2d |
|
74 |
73
|
adantr |
|
75 |
35 74
|
eqtrid |
|
76 |
|
simpr |
|
77 |
76
|
ancomd |
|
78 |
|
eqid |
|
79 |
78 12 1 11
|
coe1fvalcl |
|
80 |
77 79
|
syl |
|
81 |
65
|
eqcomd |
|
82 |
81
|
adantl |
|
83 |
82
|
fveq2d |
|
84 |
83 11
|
eqtr4di |
|
85 |
84
|
eleq2d |
|
86 |
85
|
adantr |
|
87 |
80 86
|
mpbird |
|
88 |
|
eqid |
|
89 |
|
eqid |
|
90 |
10 60 88 61 89
|
asclval |
|
91 |
87 90
|
syl |
|
92 |
1 56 49 51
|
ply1idvr1 |
|
93 |
92
|
eqcomd |
|
94 |
93
|
ad2antlr |
|
95 |
94
|
oveq2d |
|
96 |
91 95
|
eqtr2d |
|
97 |
96
|
ifeq1d |
|
98 |
97
|
adantr |
|
99 |
34 75 98
|
3eqtrd |
|