Step |
Hyp |
Ref |
Expression |
1 |
|
mdetpmtr.a |
|
2 |
|
mdetpmtr.b |
|
3 |
|
mdetpmtr.d |
|
4 |
|
mdetpmtr.g |
|
5 |
|
mdetpmtr.s |
|
6 |
|
mdetpmtr.z |
|
7 |
|
mdetpmtr.t |
|
8 |
|
mdetpmtr12.e |
|
9 |
|
mdetmptr12.r |
|
10 |
|
mdetmptr12.n |
|
11 |
|
mdetmptr12.m |
|
12 |
|
mdetmptr12.p |
|
13 |
|
mdetmptr12.q |
|
14 |
|
fveq2 |
|
15 |
14
|
oveq1d |
|
16 |
|
oveq2 |
|
17 |
15 16
|
cbvmpov |
|
18 |
1 2 3 4 5 6 7 17
|
mdetpmtr1 |
|
19 |
9 10 11 12 18
|
syl22anc |
|
20 |
|
eqid |
|
21 |
12
|
3ad2ant1 |
|
22 |
|
simp2 |
|
23 |
|
eqid |
|
24 |
23 4
|
symgfv |
|
25 |
21 22 24
|
syl2anc |
|
26 |
|
simp3 |
|
27 |
11
|
3ad2ant1 |
|
28 |
1 20 2 25 26 27
|
matecld |
|
29 |
1 20 2 10 9 28
|
matbas2d |
|
30 |
|
eqid |
|
31 |
1 2 3 4 5 6 7 30
|
mdetpmtr2 |
|
32 |
9 10 29 13 31
|
syl22anc |
|
33 |
|
simp2 |
|
34 |
13
|
3ad2ant1 |
|
35 |
|
simp3 |
|
36 |
23 4
|
symgfv |
|
37 |
34 35 36
|
syl2anc |
|
38 |
|
oveq2 |
|
39 |
|
eqid |
|
40 |
|
ovex |
|
41 |
15 38 39 40
|
ovmpo |
|
42 |
33 37 41
|
syl2anc |
|
43 |
42
|
mpoeq3dva |
|
44 |
8 43
|
eqtr4id |
|
45 |
44
|
fveq2d |
|
46 |
45
|
oveq2d |
|
47 |
32 46
|
eqtr4d |
|
48 |
47
|
oveq2d |
|
49 |
|
crngring |
|
50 |
9 49
|
syl |
|
51 |
4 5 6
|
zrhcopsgnelbas |
|
52 |
50 10 12 51
|
syl3anc |
|
53 |
4 5 6
|
zrhcopsgnelbas |
|
54 |
50 10 13 53
|
syl3anc |
|
55 |
12
|
3ad2ant1 |
|
56 |
23 4
|
symgfv |
|
57 |
55 33 56
|
syl2anc |
|
58 |
11
|
3ad2ant1 |
|
59 |
1 20 2 57 37 58
|
matecld |
|
60 |
1 20 2 10 9 59
|
matbas2d |
|
61 |
8 60
|
eqeltrid |
|
62 |
3 1 2 20
|
mdetcl |
|
63 |
9 61 62
|
syl2anc |
|
64 |
20 7
|
ringass |
|
65 |
50 52 54 63 64
|
syl13anc |
|
66 |
4 5
|
cofipsgn |
|
67 |
10 12 66
|
syl2anc |
|
68 |
4 5
|
cofipsgn |
|
69 |
10 13 68
|
syl2anc |
|
70 |
67 69
|
oveq12d |
|
71 |
6
|
zrhrhm |
|
72 |
50 71
|
syl |
|
73 |
|
1z |
|
74 |
|
neg1z |
|
75 |
|
prssi |
|
76 |
73 74 75
|
mp2an |
|
77 |
4 5
|
psgnran |
|
78 |
10 12 77
|
syl2anc |
|
79 |
76 78
|
sselid |
|
80 |
4 5
|
psgnran |
|
81 |
10 13 80
|
syl2anc |
|
82 |
76 81
|
sselid |
|
83 |
|
zringbas |
|
84 |
|
zringmulr |
|
85 |
83 84 7
|
rhmmul |
|
86 |
72 79 82 85
|
syl3anc |
|
87 |
70 86
|
eqtr4d |
|
88 |
87
|
oveq1d |
|
89 |
65 88
|
eqtr3d |
|
90 |
19 48 89
|
3eqtrd |
|