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 |
|
mdetpmtr1.e |
|
9 |
|
eqid |
|
10 |
|
eqid |
|
11 |
|
eqid |
|
12 |
|
crngring |
|
13 |
12
|
ad2antrr |
|
14 |
4
|
fvexi |
|
15 |
14
|
a1i |
|
16 |
|
simplr |
|
17 |
5 4
|
psgndmfi |
|
18 |
|
fnfun |
|
19 |
16 17 18
|
3syl |
|
20 |
|
simprr |
|
21 |
|
fndm |
|
22 |
16 17 21
|
3syl |
|
23 |
20 22
|
eleqtrrd |
|
24 |
|
fvco |
|
25 |
19 23 24
|
syl2anc |
|
26 |
4 5 6
|
zrhpsgnelbas |
|
27 |
13 16 20 26
|
syl3anc |
|
28 |
25 27
|
eqeltrd |
|
29 |
13
|
adantr |
|
30 |
4 5
|
cofipsgn |
|
31 |
16 30
|
sylan |
|
32 |
|
simpllr |
|
33 |
|
simpr |
|
34 |
4 5 6
|
zrhpsgnelbas |
|
35 |
29 32 33 34
|
syl3anc |
|
36 |
31 35
|
eqeltrd |
|
37 |
|
eqid |
|
38 |
37 9
|
mgpbas |
|
39 |
37
|
crngmgp |
|
40 |
39
|
ad3antrrr |
|
41 |
|
eqid |
|
42 |
41 4
|
symgfv |
|
43 |
42
|
adantll |
|
44 |
|
simpr |
|
45 |
|
simpll |
|
46 |
|
simp1rr |
|
47 |
|
simp2 |
|
48 |
41 4
|
symgfv |
|
49 |
46 47 48
|
syl2anc |
|
50 |
|
simp3 |
|
51 |
|
simp1rl |
|
52 |
1 9 2 49 50 51
|
matecld |
|
53 |
1 9 2 16 45 52
|
matbas2d |
|
54 |
8 53
|
eqeltrid |
|
55 |
54
|
ad2antrr |
|
56 |
1 9 2 43 44 55
|
matecld |
|
57 |
56
|
ralrimiva |
|
58 |
38 40 32 57
|
gsummptcl |
|
59 |
9 7
|
ringcl |
|
60 |
29 36 58 59
|
syl3anc |
|
61 |
|
eqid |
|
62 |
41 4
|
symgbasfi |
|
63 |
16 62
|
syl |
|
64 |
|
ovexd |
|
65 |
|
fvexd |
|
66 |
61 63 64 65
|
fsuppmptdm |
|
67 |
9 10 11 7 13 15 28 60 66
|
gsummulc2 |
|
68 |
|
nfcv |
|
69 |
|
fveq2 |
|
70 |
|
fveq1 |
|
71 |
70
|
oveq1d |
|
72 |
71
|
mpteq2dv |
|
73 |
72
|
oveq2d |
|
74 |
69 73
|
oveq12d |
|
75 |
|
ringcmn |
|
76 |
13 75
|
syl |
|
77 |
|
ssidd |
|
78 |
13
|
adantr |
|
79 |
4 5
|
cofipsgn |
|
80 |
16 79
|
sylan |
|
81 |
|
simpllr |
|
82 |
|
simpr |
|
83 |
4 5 6
|
zrhpsgnelbas |
|
84 |
78 81 82 83
|
syl3anc |
|
85 |
80 84
|
eqeltrd |
|
86 |
39
|
ad3antrrr |
|
87 |
41 4
|
symgfv |
|
88 |
87
|
adantll |
|
89 |
|
simpr |
|
90 |
|
simprl |
|
91 |
90
|
ad2antrr |
|
92 |
1 9 2 88 89 91
|
matecld |
|
93 |
92
|
ralrimiva |
|
94 |
38 86 81 93
|
gsummptcl |
|
95 |
9 7
|
ringcl |
|
96 |
78 85 94 95
|
syl3anc |
|
97 |
|
eqid |
|
98 |
41 4 97
|
symgov |
|
99 |
41 4 97
|
symgcl |
|
100 |
98 99
|
eqeltrrd |
|
101 |
20 100
|
sylan |
|
102 |
20
|
adantr |
|
103 |
4
|
symgfcoeu |
|
104 |
81 102 82 103
|
syl3anc |
|
105 |
68 9 10 74 76 63 77 96 101 104
|
gsummptf1o |
|
106 |
3 1 2 4 6 5 7 37
|
mdetleib |
|
107 |
106
|
ad2antrl |
|
108 |
28
|
adantr |
|
109 |
9 7
|
ringass |
|
110 |
29 108 36 58 109
|
syl13anc |
|
111 |
25
|
adantr |
|
112 |
111 31
|
oveq12d |
|
113 |
4 5
|
cofipsgn |
|
114 |
32 101 113
|
syl2anc |
|
115 |
20
|
adantr |
|
116 |
41 5 4
|
psgnco |
|
117 |
32 115 33 116
|
syl3anc |
|
118 |
117
|
fveq2d |
|
119 |
6
|
zrhrhm |
|
120 |
13 119
|
syl |
|
121 |
120
|
adantr |
|
122 |
|
1z |
|
123 |
|
neg1z |
|
124 |
|
prssi |
|
125 |
122 123 124
|
mp2an |
|
126 |
4 5
|
psgnran |
|
127 |
32 115 126
|
syl2anc |
|
128 |
125 127
|
sseldi |
|
129 |
4 5
|
psgnran |
|
130 |
16 129
|
sylan |
|
131 |
125 130
|
sseldi |
|
132 |
|
zringbas |
|
133 |
|
zringmulr |
|
134 |
132 133 7
|
rhmmul |
|
135 |
121 128 131 134
|
syl3anc |
|
136 |
114 118 135
|
3eqtrrd |
|
137 |
112 136
|
eqtrd |
|
138 |
8
|
a1i |
|
139 |
|
simprl |
|
140 |
139
|
fveq2d |
|
141 |
|
simpllr |
|
142 |
41 4
|
symgbasf |
|
143 |
|
ffun |
|
144 |
141 142 143
|
3syl |
|
145 |
|
simplr |
|
146 |
|
fdm |
|
147 |
141 142 146
|
3syl |
|
148 |
145 147
|
eleqtrrd |
|
149 |
|
fvco |
|
150 |
144 148 149
|
syl2anc |
|
151 |
140 150
|
eqtr4d |
|
152 |
|
simprr |
|
153 |
151 152
|
oveq12d |
|
154 |
|
ovexd |
|
155 |
138 153 43 44 154
|
ovmpod |
|
156 |
155
|
mpteq2dva |
|
157 |
156
|
oveq2d |
|
158 |
137 157
|
oveq12d |
|
159 |
110 158
|
eqtr3d |
|
160 |
159
|
mpteq2dva |
|
161 |
160
|
oveq2d |
|
162 |
105 107 161
|
3eqtr4d |
|
163 |
3 1 2 4 6 5 7 37
|
mdetleib |
|
164 |
54 163
|
syl |
|
165 |
164
|
oveq2d |
|
166 |
67 162 165
|
3eqtr4d |
|