Step |
Hyp |
Ref |
Expression |
1 |
|
madjusmdet.b |
|
2 |
|
madjusmdet.a |
|
3 |
|
madjusmdet.d |
|
4 |
|
madjusmdet.k |
|
5 |
|
madjusmdet.t |
|
6 |
|
madjusmdet.z |
|
7 |
|
madjusmdet.e |
|
8 |
|
madjusmdet.n |
|
9 |
|
madjusmdet.r |
|
10 |
|
madjusmdet.i |
|
11 |
|
madjusmdet.j |
|
12 |
|
madjusmdet.m |
|
13 |
|
madjusmdetlem1.g |
|
14 |
|
madjusmdetlem1.s |
|
15 |
|
madjusmdetlem1.u |
|
16 |
|
madjusmdetlem1.w |
|
17 |
|
madjusmdetlem1.p |
|
18 |
|
madjusmdetlem1.q |
|
19 |
|
madjusmdetlem1.1 |
|
20 |
|
madjusmdetlem1.2 |
|
21 |
|
madjusmdetlem1.3 |
|
22 |
2 1 3 4
|
maducoevalmin1 |
|
23 |
12 11 10 22
|
syl3anc |
|
24 |
15
|
fveq2i |
|
25 |
23 24
|
eqtr4di |
|
26 |
|
fzfid |
|
27 |
|
crngring |
|
28 |
9 27
|
syl |
|
29 |
2 1
|
minmar1cl |
|
30 |
28 12 10 11 29
|
syl22anc |
|
31 |
15 30
|
eqeltrid |
|
32 |
2 1 3 13 14 6 5 16 9 26 31 17 18
|
mdetpmtr12 |
|
33 |
|
simplr |
|
34 |
33
|
fveq2d |
|
35 |
19
|
3ad2ant1 |
|
36 |
35
|
ad2antrr |
|
37 |
34 36
|
eqtrd |
|
38 |
|
simpr |
|
39 |
38
|
fveq2d |
|
40 |
20
|
3ad2ant1 |
|
41 |
40
|
ad2antrr |
|
42 |
39 41
|
eqtrd |
|
43 |
37 42
|
oveq12d |
|
44 |
12
|
3ad2ant1 |
|
45 |
44
|
ad2antrr |
|
46 |
10
|
3ad2ant1 |
|
47 |
46
|
ad2antrr |
|
48 |
11
|
3ad2ant1 |
|
49 |
48
|
ad2antrr |
|
50 |
|
eqid |
|
51 |
|
eqid |
|
52 |
|
eqid |
|
53 |
2 1 50 51 52
|
minmar1eval |
|
54 |
45 47 49 47 49 53
|
syl122anc |
|
55 |
|
eqid |
|
56 |
55
|
iftruei |
|
57 |
|
eqid |
|
58 |
57
|
iftruei |
|
59 |
56 58
|
eqtri |
|
60 |
59
|
a1i |
|
61 |
43 54 60
|
3eqtrrd |
|
62 |
|
simplr |
|
63 |
62
|
fveq2d |
|
64 |
35
|
ad2antrr |
|
65 |
63 64
|
eqtrd |
|
66 |
65
|
oveq1d |
|
67 |
44
|
ad2antrr |
|
68 |
46
|
ad2antrr |
|
69 |
48
|
ad2antrr |
|
70 |
18
|
3ad2ant1 |
|
71 |
|
simp3 |
|
72 |
|
eqid |
|
73 |
72 13
|
symgfv |
|
74 |
70 71 73
|
syl2anc |
|
75 |
74
|
ad2antrr |
|
76 |
2 1 50 51 52
|
minmar1eval |
|
77 |
67 68 69 68 75 76
|
syl122anc |
|
78 |
55
|
a1i |
|
79 |
78
|
iftrued |
|
80 |
|
simpr |
|
81 |
80
|
fveq2d |
|
82 |
72 13
|
symgbasf1o |
|
83 |
70 82
|
syl |
|
84 |
83
|
ad2antrr |
|
85 |
71
|
ad2antrr |
|
86 |
|
f1ocnvfv1 |
|
87 |
84 85 86
|
syl2anc |
|
88 |
20
|
fveq2d |
|
89 |
18 82
|
syl |
|
90 |
|
nnuz |
|
91 |
8 90
|
eleqtrdi |
|
92 |
|
eluzfz2 |
|
93 |
91 92
|
syl |
|
94 |
|
f1ocnvfv1 |
|
95 |
89 93 94
|
syl2anc |
|
96 |
88 95
|
eqtr3d |
|
97 |
96
|
3ad2ant1 |
|
98 |
97
|
ad2antrr |
|
99 |
81 87 98
|
3eqtr3d |
|
100 |
99
|
ex |
|
101 |
100
|
con3d |
|
102 |
101
|
imp |
|
103 |
102
|
iffalsed |
|
104 |
79 103
|
eqtrd |
|
105 |
66 77 104
|
3eqtrrd |
|
106 |
61 105
|
ifeqda |
|
107 |
|
simp2 |
|
108 |
107
|
adantr |
|
109 |
71
|
adantr |
|
110 |
|
ovexd |
|
111 |
15
|
oveqi |
|
112 |
111
|
a1i |
|
113 |
112
|
mpoeq3ia |
|
114 |
16 113
|
eqtri |
|
115 |
114
|
ovmpt4g |
|
116 |
108 109 110 115
|
syl3anc |
|
117 |
106 116
|
ifeqda |
|
118 |
117
|
mpoeq3dva |
|
119 |
|
eqid |
|
120 |
17
|
3ad2ant1 |
|
121 |
72 13
|
symgfv |
|
122 |
120 107 121
|
syl2anc |
|
123 |
31
|
3ad2ant1 |
|
124 |
2 119 1 122 74 123
|
matecld |
|
125 |
2 119 1 26 9 124
|
matbas2d |
|
126 |
16 125
|
eqeltrid |
|
127 |
119 51
|
ringidcl |
|
128 |
28 127
|
syl |
|
129 |
|
eqid |
|
130 |
2 1 129 52
|
marrepval |
|
131 |
126 128 93 93 130
|
syl22anc |
|
132 |
114
|
a1i |
|
133 |
118 131 132
|
3eqtr4d |
|
134 |
133
|
fveq2d |
|
135 |
|
eqid |
|
136 |
2 135 1
|
submaval |
|
137 |
126 93 93 136
|
syl3anc |
|
138 |
|
fzdif2 |
|
139 |
91 138
|
syl |
|
140 |
|
mpoeq12 |
|
141 |
139 139 140
|
syl2anc |
|
142 |
137 141
|
eqtrd |
|
143 |
|
difssd |
|
144 |
139 143
|
eqsstrrd |
|
145 |
2 1
|
submabas |
|
146 |
126 144 145
|
syl2anc |
|
147 |
142 146
|
eqeltrd |
|
148 |
|
eqid |
|
149 |
|
eqid |
|
150 |
7 148 149 119
|
mdetcl |
|
151 |
9 147 150
|
syl2anc |
|
152 |
119 5 51
|
ringlidm |
|
153 |
28 151 152
|
syl2anc |
|
154 |
2
|
fveq2i |
|
155 |
1 154
|
eqtri |
|
156 |
126 155
|
eleqtrdi |
|
157 |
|
smadiadetr |
|
158 |
9 156 93 128 157
|
syl22anc |
|
159 |
3
|
fveq1i |
|
160 |
5
|
oveqi |
|
161 |
159 160
|
eqeq12i |
|
162 |
158 161
|
sylibr |
|
163 |
139
|
oveq1d |
|
164 |
163 7
|
eqtr4di |
|
165 |
164
|
fveq1d |
|
166 |
165
|
oveq2d |
|
167 |
162 166
|
eqtrd |
|
168 |
2 1
|
submat1n |
|
169 |
8 126 168
|
syl2anc |
|
170 |
169
|
fveq2d |
|
171 |
153 167 170
|
3eqtr4d |
|
172 |
134 171
|
eqtr3d |
|
173 |
2 1 8 10 11 28 12 15
|
submatminr1 |
|
174 |
173 21
|
eqtrd |
|
175 |
174
|
fveq2d |
|
176 |
172 175
|
eqtr4d |
|
177 |
176
|
oveq2d |
|
178 |
25 32 177
|
3eqtrd |
|