Step |
Hyp |
Ref |
Expression |
1 |
|
mdetrlin.d |
|
2 |
|
mdetrlin.a |
|
3 |
|
mdetrlin.b |
|
4 |
|
mdetrlin.p |
|
5 |
|
mdetrlin.r |
|
6 |
|
mdetrlin.x |
|
7 |
|
mdetrlin.y |
|
8 |
|
mdetrlin.z |
|
9 |
|
mdetrlin.i |
|
10 |
|
mdetrlin.eq |
|
11 |
|
mdetrlin.ne1 |
|
12 |
|
mdetrlin.ne2 |
|
13 |
|
fvex |
|
14 |
|
ovex |
|
15 |
|
eqid |
|
16 |
14 15
|
fnmpti |
|
17 |
|
ovex |
|
18 |
|
eqid |
|
19 |
17 18
|
fnmpti |
|
20 |
|
ofmpteq |
|
21 |
13 16 19 20
|
mp3an |
|
22 |
|
crngring |
|
23 |
5 22
|
syl |
|
24 |
23
|
adantr |
|
25 |
2 3
|
matrcl |
|
26 |
7 25
|
syl |
|
27 |
26
|
simpld |
|
28 |
|
zrhpsgnmhm |
|
29 |
23 27 28
|
syl2anc |
|
30 |
|
eqid |
|
31 |
|
eqid |
|
32 |
|
eqid |
|
33 |
31 32
|
mgpbas |
|
34 |
30 33
|
mhmf |
|
35 |
29 34
|
syl |
|
36 |
35
|
ffvelrnda |
|
37 |
31
|
crngmgp |
|
38 |
5 37
|
syl |
|
39 |
38
|
adantr |
|
40 |
27
|
adantr |
|
41 |
2 32 3
|
matbas2i |
|
42 |
|
elmapi |
|
43 |
7 41 42
|
3syl |
|
44 |
43
|
ad2antrr |
|
45 |
|
simpr |
|
46 |
|
eqid |
|
47 |
46 30
|
symgbasf |
|
48 |
47
|
adantl |
|
49 |
48
|
ffvelrnda |
|
50 |
44 45 49
|
fovrnd |
|
51 |
50
|
ralrimiva |
|
52 |
33 39 40 51
|
gsummptcl |
|
53 |
2 32 3
|
matbas2i |
|
54 |
|
elmapi |
|
55 |
8 53 54
|
3syl |
|
56 |
55
|
ad2antrr |
|
57 |
56 45 49
|
fovrnd |
|
58 |
57
|
ralrimiva |
|
59 |
33 39 40 58
|
gsummptcl |
|
60 |
|
eqid |
|
61 |
32 4 60
|
ringdi |
|
62 |
24 36 52 59 61
|
syl13anc |
|
63 |
|
cmnmnd |
|
64 |
39 63
|
syl |
|
65 |
9
|
adantr |
|
66 |
43
|
adantr |
|
67 |
48 65
|
ffvelrnd |
|
68 |
66 65 67
|
fovrnd |
|
69 |
|
id |
|
70 |
|
fveq2 |
|
71 |
69 70
|
oveq12d |
|
72 |
33 71
|
gsumsn |
|
73 |
64 65 68 72
|
syl3anc |
|
74 |
73 68
|
eqeltrd |
|
75 |
55
|
adantr |
|
76 |
75 65 67
|
fovrnd |
|
77 |
69 70
|
oveq12d |
|
78 |
33 77
|
gsumsn |
|
79 |
64 65 76 78
|
syl3anc |
|
80 |
79 76
|
eqeltrd |
|
81 |
|
difssd |
|
82 |
40 81
|
ssfid |
|
83 |
|
eldifi |
|
84 |
2 32 3
|
matbas2i |
|
85 |
|
elmapi |
|
86 |
6 84 85
|
3syl |
|
87 |
86
|
ad2antrr |
|
88 |
87 45 49
|
fovrnd |
|
89 |
83 88
|
sylan2 |
|
90 |
89
|
ralrimiva |
|
91 |
33 39 82 90
|
gsummptcl |
|
92 |
32 4 60
|
ringdir |
|
93 |
24 74 80 91 92
|
syl13anc |
|
94 |
31 60
|
mgpplusg |
|
95 |
|
disjdif |
|
96 |
95
|
a1i |
|
97 |
9
|
snssd |
|
98 |
97
|
adantr |
|
99 |
|
undif |
|
100 |
98 99
|
sylib |
|
101 |
100
|
eqcomd |
|
102 |
33 94 39 40 88 96 101
|
gsummptfidmsplit |
|
103 |
10
|
adantr |
|
104 |
103
|
oveqd |
|
105 |
|
xpss1 |
|
106 |
98 105
|
syl |
|
107 |
66 106
|
fssresd |
|
108 |
107
|
ffnd |
|
109 |
75 106
|
fssresd |
|
110 |
109
|
ffnd |
|
111 |
|
snex |
|
112 |
|
xpexg |
|
113 |
111 40 112
|
sylancr |
|
114 |
|
snidg |
|
115 |
65 114
|
syl |
|
116 |
115 67
|
opelxpd |
|
117 |
|
fnfvof |
|
118 |
108 110 113 116 117
|
syl22anc |
|
119 |
|
df-ov |
|
120 |
|
df-ov |
|
121 |
|
df-ov |
|
122 |
120 121
|
oveq12i |
|
123 |
118 119 122
|
3eqtr4g |
|
124 |
104 123
|
eqtrd |
|
125 |
|
ovres |
|
126 |
115 67 125
|
syl2anc |
|
127 |
|
ovres |
|
128 |
115 67 127
|
syl2anc |
|
129 |
|
ovres |
|
130 |
115 67 129
|
syl2anc |
|
131 |
128 130
|
oveq12d |
|
132 |
124 126 131
|
3eqtr3d |
|
133 |
86
|
adantr |
|
134 |
133 65 67
|
fovrnd |
|
135 |
69 70
|
oveq12d |
|
136 |
33 135
|
gsumsn |
|
137 |
64 65 134 136
|
syl3anc |
|
138 |
73 79
|
oveq12d |
|
139 |
132 137 138
|
3eqtr4d |
|
140 |
139
|
oveq1d |
|
141 |
102 140
|
eqtrd |
|
142 |
33 94 39 40 50 96 101
|
gsummptfidmsplit |
|
143 |
11
|
ad2antrr |
|
144 |
143
|
oveqd |
|
145 |
|
simpr |
|
146 |
83 49
|
sylan2 |
|
147 |
|
ovres |
|
148 |
145 146 147
|
syl2anc |
|
149 |
|
ovres |
|
150 |
145 146 149
|
syl2anc |
|
151 |
144 148 150
|
3eqtr3rd |
|
152 |
151
|
mpteq2dva |
|
153 |
152
|
oveq2d |
|
154 |
153
|
oveq2d |
|
155 |
142 154
|
eqtrd |
|
156 |
33 94 39 40 57 96 101
|
gsummptfidmsplit |
|
157 |
12
|
ad2antrr |
|
158 |
157
|
oveqd |
|
159 |
|
ovres |
|
160 |
145 146 159
|
syl2anc |
|
161 |
158 148 160
|
3eqtr3rd |
|
162 |
161
|
mpteq2dva |
|
163 |
162
|
oveq2d |
|
164 |
163
|
oveq2d |
|
165 |
156 164
|
eqtrd |
|
166 |
155 165
|
oveq12d |
|
167 |
93 141 166
|
3eqtr4rd |
|
168 |
167
|
oveq2d |
|
169 |
62 168
|
eqtr3d |
|
170 |
169
|
mpteq2dva |
|
171 |
21 170
|
eqtrid |
|
172 |
171
|
oveq2d |
|
173 |
|
ringcmn |
|
174 |
5 22 173
|
3syl |
|
175 |
46 30
|
symgbasfi |
|
176 |
27 175
|
syl |
|
177 |
32 60
|
ringcl |
|
178 |
24 36 52 177
|
syl3anc |
|
179 |
32 60
|
ringcl |
|
180 |
24 36 59 179
|
syl3anc |
|
181 |
32 4 174 176 178 180 15 18
|
gsummptfidmadd2 |
|
182 |
172 181
|
eqtr3d |
|
183 |
|
eqid |
|
184 |
|
eqid |
|
185 |
1 2 3 30 183 184 60 31
|
mdetleib2 |
|
186 |
5 6 185
|
syl2anc |
|
187 |
1 2 3 30 183 184 60 31
|
mdetleib2 |
|
188 |
5 7 187
|
syl2anc |
|
189 |
1 2 3 30 183 184 60 31
|
mdetleib2 |
|
190 |
5 8 189
|
syl2anc |
|
191 |
188 190
|
oveq12d |
|
192 |
182 186 191
|
3eqtr4d |
|