Step |
Hyp |
Ref |
Expression |
1 |
|
minvec.x |
|
2 |
|
minvec.m |
|
3 |
|
minvec.n |
|
4 |
|
minvec.u |
|
5 |
|
minvec.y |
|
6 |
|
minvec.w |
|
7 |
|
minvec.a |
|
8 |
|
minvec.j |
|
9 |
|
minvec.r |
|
10 |
|
minvec.s |
|
11 |
|
minvec.d |
|
12 |
|
minvec.f |
|
13 |
|
ssrab2 |
|
14 |
5
|
adantr |
|
15 |
|
elpw2g |
|
16 |
14 15
|
syl |
|
17 |
13 16
|
mpbiri |
|
18 |
17
|
fmpttd |
|
19 |
18
|
frnd |
|
20 |
12 19
|
eqsstrid |
|
21 |
|
1rp |
|
22 |
|
eqid |
|
23 |
22 17
|
dmmptd |
|
24 |
21 23
|
eleqtrrid |
|
25 |
24
|
ne0d |
|
26 |
|
dm0rn0 |
|
27 |
12
|
eqeq1i |
|
28 |
26 27
|
bitr4i |
|
29 |
28
|
necon3bii |
|
30 |
25 29
|
sylib |
|
31 |
1 2 3 4 5 6 7 8 9 10
|
minveclem4c |
|
32 |
31
|
resqcld |
|
33 |
|
ltaddrp |
|
34 |
32 33
|
sylan |
|
35 |
32
|
adantr |
|
36 |
|
rpre |
|
37 |
36
|
adantl |
|
38 |
35 37
|
readdcld |
|
39 |
38
|
recnd |
|
40 |
39
|
sqsqrtd |
|
41 |
34 40
|
breqtrrd |
|
42 |
1 2 3 4 5 6 7 8 9
|
minveclem1 |
|
43 |
42
|
simp1d |
|
44 |
43
|
adantr |
|
45 |
42
|
simp2d |
|
46 |
45
|
adantr |
|
47 |
|
0re |
|
48 |
42
|
simp3d |
|
49 |
|
breq1 |
|
50 |
49
|
ralbidv |
|
51 |
50
|
rspcev |
|
52 |
47 48 51
|
sylancr |
|
53 |
52
|
adantr |
|
54 |
|
infrecl |
|
55 |
44 46 53 54
|
syl3anc |
|
56 |
10 55
|
eqeltrid |
|
57 |
|
0red |
|
58 |
56
|
sqge0d |
|
59 |
57 35 38 58 34
|
lelttrd |
|
60 |
57 38 59
|
ltled |
|
61 |
38 60
|
resqrtcld |
|
62 |
48
|
adantr |
|
63 |
|
infregelb |
|
64 |
44 46 53 57 63
|
syl31anc |
|
65 |
62 64
|
mpbird |
|
66 |
65 10
|
breqtrrdi |
|
67 |
38 60
|
sqrtge0d |
|
68 |
56 61 66 67
|
lt2sqd |
|
69 |
41 68
|
mpbird |
|
70 |
56 61
|
ltnled |
|
71 |
69 70
|
mpbid |
|
72 |
10
|
breq2i |
|
73 |
|
infregelb |
|
74 |
44 46 53 61 73
|
syl31anc |
|
75 |
9
|
raleqi |
|
76 |
|
fvex |
|
77 |
76
|
rgenw |
|
78 |
|
eqid |
|
79 |
|
breq2 |
|
80 |
78 79
|
ralrnmptw |
|
81 |
77 80
|
ax-mp |
|
82 |
75 81
|
bitri |
|
83 |
74 82
|
bitrdi |
|
84 |
72 83
|
syl5bb |
|
85 |
71 84
|
mtbid |
|
86 |
|
rexnal |
|
87 |
85 86
|
sylibr |
|
88 |
61
|
adantr |
|
89 |
|
cphngp |
|
90 |
4 89
|
syl |
|
91 |
|
ngpms |
|
92 |
1 11
|
msmet |
|
93 |
90 91 92
|
3syl |
|
94 |
93
|
ad2antrr |
|
95 |
7
|
ad2antrr |
|
96 |
|
eqid |
|
97 |
1 96
|
lssss |
|
98 |
14 97
|
syl |
|
99 |
98
|
sselda |
|
100 |
|
metcl |
|
101 |
94 95 99 100
|
syl3anc |
|
102 |
67
|
adantr |
|
103 |
|
metge0 |
|
104 |
94 95 99 103
|
syl3anc |
|
105 |
88 101 102 104
|
le2sqd |
|
106 |
11
|
oveqi |
|
107 |
95 99
|
ovresd |
|
108 |
106 107
|
syl5eq |
|
109 |
90
|
ad2antrr |
|
110 |
|
eqid |
|
111 |
3 1 2 110
|
ngpds |
|
112 |
109 95 99 111
|
syl3anc |
|
113 |
108 112
|
eqtrd |
|
114 |
113
|
breq2d |
|
115 |
40
|
adantr |
|
116 |
115
|
breq1d |
|
117 |
105 114 116
|
3bitr3d |
|
118 |
117
|
notbid |
|
119 |
38
|
adantr |
|
120 |
101
|
resqcld |
|
121 |
119 120
|
letrid |
|
122 |
121
|
ord |
|
123 |
118 122
|
sylbid |
|
124 |
123
|
reximdva |
|
125 |
87 124
|
mpd |
|
126 |
|
rabn0 |
|
127 |
125 126
|
sylibr |
|
128 |
127
|
necomd |
|
129 |
128
|
neneqd |
|
130 |
129
|
nrexdv |
|
131 |
12
|
eleq2i |
|
132 |
|
0ex |
|
133 |
22
|
elrnmpt |
|
134 |
132 133
|
ax-mp |
|
135 |
131 134
|
bitri |
|
136 |
130 135
|
sylnibr |
|
137 |
|
df-nel |
|
138 |
136 137
|
sylibr |
|
139 |
56
|
adantr |
|
140 |
139
|
resqcld |
|
141 |
37
|
adantr |
|
142 |
120 140 141
|
lesubadd2d |
|
143 |
142
|
rabbidva |
|
144 |
143
|
mpteq2dva |
|
145 |
144
|
rneqd |
|
146 |
12 145
|
eqtr4id |
|
147 |
146
|
eleq2d |
|
148 |
|
breq2 |
|
149 |
148
|
rabbidv |
|
150 |
149
|
cbvmptv |
|
151 |
150
|
elrnmpt |
|
152 |
151
|
elv |
|
153 |
147 152
|
bitrdi |
|
154 |
146
|
eleq2d |
|
155 |
|
breq2 |
|
156 |
155
|
rabbidv |
|
157 |
156
|
cbvmptv |
|
158 |
157
|
elrnmpt |
|
159 |
158
|
elv |
|
160 |
154 159
|
bitrdi |
|
161 |
153 160
|
anbi12d |
|
162 |
|
reeanv |
|
163 |
93
|
ad2antrr |
|
164 |
7
|
ad2antrr |
|
165 |
5 97
|
syl |
|
166 |
165
|
adantr |
|
167 |
166
|
sselda |
|
168 |
163 164 167 100
|
syl3anc |
|
169 |
168
|
resqcld |
|
170 |
32
|
ad2antrr |
|
171 |
169 170
|
resubcld |
|
172 |
|
simplrl |
|
173 |
172
|
rpred |
|
174 |
|
simplrr |
|
175 |
174
|
rpred |
|
176 |
|
lemin |
|
177 |
171 173 175 176
|
syl3anc |
|
178 |
177
|
rabbidva |
|
179 |
|
ifcl |
|
180 |
5
|
adantr |
|
181 |
|
rabexg |
|
182 |
180 181
|
syl |
|
183 |
|
eqid |
|
184 |
|
breq2 |
|
185 |
184
|
rabbidv |
|
186 |
183 185
|
elrnmpt1s |
|
187 |
179 182 186
|
syl2an2 |
|
188 |
146
|
adantr |
|
189 |
187 188
|
eleqtrrd |
|
190 |
178 189
|
eqeltrrd |
|
191 |
|
ineq12 |
|
192 |
|
inrab |
|
193 |
191 192
|
eqtrdi |
|
194 |
193
|
eleq1d |
|
195 |
190 194
|
syl5ibrcom |
|
196 |
|
vex |
|
197 |
196
|
inex1 |
|
198 |
197
|
pwid |
|
199 |
|
inelcm |
|
200 |
198 199
|
mpan2 |
|
201 |
195 200
|
syl6 |
|
202 |
201
|
rexlimdvva |
|
203 |
162 202
|
syl5bir |
|
204 |
161 203
|
sylbid |
|
205 |
204
|
ralrimivv |
|
206 |
30 138 205
|
3jca |
|
207 |
|
isfbas |
|
208 |
5 207
|
syl |
|
209 |
20 206 208
|
mpbir2and |
|