Step |
Hyp |
Ref |
Expression |
1 |
|
hoidmv1lelem1.a |
|
2 |
|
hoidmv1lelem1.b |
|
3 |
|
hoidmv1lelem1.l |
|
4 |
|
hoidmv1lelem1.c |
|
5 |
|
hoidmv1lelem1.d |
|
6 |
|
hoidmv1lelem1.r |
|
7 |
|
hoidmv1lelem1.u |
|
8 |
|
hoidmv1lelem1.s |
|
9 |
|
ssrab2 |
|
10 |
7 9
|
eqsstri |
|
11 |
10
|
a1i |
|
12 |
1
|
rexrd |
|
13 |
2
|
rexrd |
|
14 |
1 2 3
|
ltled |
|
15 |
|
lbicc2 |
|
16 |
12 13 14 15
|
syl3anc |
|
17 |
1
|
recnd |
|
18 |
17
|
subidd |
|
19 |
|
nfv |
|
20 |
|
nnex |
|
21 |
20
|
a1i |
|
22 |
|
volf |
|
23 |
22
|
a1i |
|
24 |
4
|
ffvelrnda |
|
25 |
5
|
ffvelrnda |
|
26 |
1
|
adantr |
|
27 |
25 26
|
ifcld |
|
28 |
27
|
rexrd |
|
29 |
|
icombl |
|
30 |
24 28 29
|
syl2anc |
|
31 |
23 30
|
ffvelrnd |
|
32 |
19 21 31
|
sge0ge0mpt |
|
33 |
18 32
|
eqbrtrd |
|
34 |
16 33
|
jca |
|
35 |
|
oveq1 |
|
36 |
|
breq2 |
|
37 |
|
id |
|
38 |
36 37
|
ifbieq2d |
|
39 |
38
|
oveq2d |
|
40 |
39
|
fveq2d |
|
41 |
40
|
mpteq2dv |
|
42 |
41
|
fveq2d |
|
43 |
35 42
|
breq12d |
|
44 |
43
|
elrab |
|
45 |
34 44
|
sylibr |
|
46 |
45 7
|
eleqtrrdi |
|
47 |
46
|
ne0d |
|
48 |
1 2 11 47
|
supicc |
|
49 |
8 48
|
eqeltrid |
|
50 |
8
|
a1i |
|
51 |
|
nfv |
|
52 |
1 2
|
iccssred |
|
53 |
11 52
|
sstrd |
|
54 |
53
|
sselda |
|
55 |
|
nfv |
|
56 |
20
|
a1i |
|
57 |
22
|
a1i |
|
58 |
24
|
adantlr |
|
59 |
25
|
adantlr |
|
60 |
54
|
adantr |
|
61 |
59 60
|
ifcld |
|
62 |
61
|
rexrd |
|
63 |
|
icombl |
|
64 |
58 62 63
|
syl2anc |
|
65 |
57 64
|
ffvelrnd |
|
66 |
55 56 65
|
sge0xrclmpt |
|
67 |
|
pnfxr |
|
68 |
67
|
a1i |
|
69 |
6
|
rexrd |
|
70 |
69
|
adantr |
|
71 |
25
|
rexrd |
|
72 |
|
icombl |
|
73 |
24 71 72
|
syl2anc |
|
74 |
23 73
|
ffvelrnd |
|
75 |
74
|
adantlr |
|
76 |
73
|
adantlr |
|
77 |
24
|
rexrd |
|
78 |
77
|
adantlr |
|
79 |
71
|
adantlr |
|
80 |
24
|
leidd |
|
81 |
80
|
adantlr |
|
82 |
|
min1 |
|
83 |
59 60 82
|
syl2anc |
|
84 |
|
icossico |
|
85 |
78 79 81 83 84
|
syl22anc |
|
86 |
|
volss |
|
87 |
64 76 85 86
|
syl3anc |
|
88 |
55 56 65 75 87
|
sge0lempt |
|
89 |
6
|
ltpnfd |
|
90 |
89
|
adantr |
|
91 |
66 70 68 88 90
|
xrlelttrd |
|
92 |
66 68 91
|
xrltned |
|
93 |
92
|
neneqd |
|
94 |
|
eqid |
|
95 |
65 94
|
fmptd |
|
96 |
56 95
|
sge0repnf |
|
97 |
93 96
|
mpbird |
|
98 |
1
|
adantr |
|
99 |
97 98
|
readdcld |
|
100 |
52 49
|
sseldd |
|
101 |
100
|
adantr |
|
102 |
25 101
|
ifcld |
|
103 |
102
|
rexrd |
|
104 |
|
icombl |
|
105 |
24 103 104
|
syl2anc |
|
106 |
23 105
|
ffvelrnd |
|
107 |
19 21 106
|
sge0xrclmpt |
|
108 |
67
|
a1i |
|
109 |
|
min1 |
|
110 |
25 101 109
|
syl2anc |
|
111 |
|
icossico |
|
112 |
77 71 80 110 111
|
syl22anc |
|
113 |
|
volss |
|
114 |
105 73 112 113
|
syl3anc |
|
115 |
19 21 106 74 114
|
sge0lempt |
|
116 |
107 69 108 115 89
|
xrlelttrd |
|
117 |
107 108 116
|
xrltned |
|
118 |
117
|
neneqd |
|
119 |
|
eqid |
|
120 |
106 119
|
fmptd |
|
121 |
21 120
|
sge0repnf |
|
122 |
118 121
|
mpbird |
|
123 |
122 1
|
readdcld |
|
124 |
123
|
adantr |
|
125 |
7
|
eleq2i |
|
126 |
125
|
biimpi |
|
127 |
126
|
adantl |
|
128 |
|
rabid |
|
129 |
127 128
|
sylib |
|
130 |
129
|
simprd |
|
131 |
54 98 97
|
lesubaddd |
|
132 |
130 131
|
mpbid |
|
133 |
122
|
adantr |
|
134 |
106
|
adantlr |
|
135 |
105
|
adantlr |
|
136 |
103
|
adantlr |
|
137 |
61
|
adantr |
|
138 |
|
eqidd |
|
139 |
|
iftrue |
|
140 |
139
|
adantl |
|
141 |
59
|
adantr |
|
142 |
60
|
adantr |
|
143 |
100
|
ad3antrrr |
|
144 |
|
simpr |
|
145 |
53
|
adantr |
|
146 |
47
|
adantr |
|
147 |
1 2
|
jca |
|
148 |
|
iccsupr |
|
149 |
147 11 46 148
|
syl3anc |
|
150 |
149
|
simp3d |
|
151 |
150
|
adantr |
|
152 |
127 125
|
sylibr |
|
153 |
|
suprub |
|
154 |
145 146 151 152 153
|
syl31anc |
|
155 |
154 8
|
breqtrrdi |
|
156 |
155
|
ad2antrr |
|
157 |
141 142 143 144 156
|
letrd |
|
158 |
157
|
iftrued |
|
159 |
138 140 158
|
3eqtr4d |
|
160 |
137 159
|
eqled |
|
161 |
60
|
adantr |
|
162 |
59
|
adantr |
|
163 |
|
simpr |
|
164 |
161 162
|
ltnled |
|
165 |
163 164
|
mpbird |
|
166 |
161 162 165
|
ltled |
|
167 |
166
|
adantr |
|
168 |
|
iffalse |
|
169 |
168
|
ad2antlr |
|
170 |
|
iftrue |
|
171 |
170
|
adantl |
|
172 |
169 171
|
breq12d |
|
173 |
167 172
|
mpbird |
|
174 |
155
|
ad3antrrr |
|
175 |
168
|
ad2antlr |
|
176 |
|
iffalse |
|
177 |
176
|
adantl |
|
178 |
175 177
|
breq12d |
|
179 |
174 178
|
mpbird |
|
180 |
173 179
|
pm2.61dan |
|
181 |
160 180
|
pm2.61dan |
|
182 |
|
icossico |
|
183 |
78 136 81 181 182
|
syl22anc |
|
184 |
|
volss |
|
185 |
64 135 183 184
|
syl3anc |
|
186 |
55 56 65 134 185
|
sge0lempt |
|
187 |
97 133 98 186
|
leadd1dd |
|
188 |
54 99 124 132 187
|
letrd |
|
189 |
188
|
ex |
|
190 |
51 189
|
ralrimi |
|
191 |
|
suprleub |
|
192 |
53 47 150 123 191
|
syl31anc |
|
193 |
190 192
|
mpbird |
|
194 |
50 193
|
eqbrtrd |
|
195 |
100 1 122
|
lesubaddd |
|
196 |
194 195
|
mpbird |
|
197 |
49 196
|
jca |
|
198 |
|
oveq1 |
|
199 |
|
breq2 |
|
200 |
|
id |
|
201 |
199 200
|
ifbieq2d |
|
202 |
201
|
oveq2d |
|
203 |
202
|
fveq2d |
|
204 |
203
|
mpteq2dv |
|
205 |
204
|
fveq2d |
|
206 |
198 205
|
breq12d |
|
207 |
206
|
elrab |
|
208 |
197 207
|
sylibr |
|
209 |
208 7
|
eleqtrrdi |
|
210 |
209 46 150
|
3jca |
|