Step |
Hyp |
Ref |
Expression |
1 |
|
dihopelvalcp.b |
|
2 |
|
dihopelvalcp.l |
|
3 |
|
dihopelvalcp.j |
|
4 |
|
dihopelvalcp.m |
|
5 |
|
dihopelvalcp.a |
|
6 |
|
dihopelvalcp.h |
|
7 |
|
dihopelvalcp.p |
|
8 |
|
dihopelvalcp.t |
|
9 |
|
dihopelvalcp.r |
|
10 |
|
dihopelvalcp.e |
|
11 |
|
dihopelvalcp.i |
|
12 |
|
dihopelvalcp.g |
|
13 |
|
dihopelvalcp.f |
|
14 |
|
dihopelvalcp.s |
|
15 |
|
dihopelvalcp.z |
|
16 |
|
dihopelvalcp.n |
|
17 |
|
dihopelvalcp.c |
|
18 |
|
dihopelvalcp.u |
|
19 |
|
dihopelvalcp.d |
|
20 |
|
dihopelvalcp.v |
|
21 |
|
dihopelvalcp.y |
|
22 |
|
dihopelvalcp.o |
|
23 |
1 2 3 4 5 6 11 16 17 18 21
|
dihvalcq |
|
24 |
23
|
eleq2d |
|
25 |
|
simp1 |
|
26 |
|
simp3l |
|
27 |
2 5 6 18 17 20
|
diclss |
|
28 |
25 26 27
|
syl2anc |
|
29 |
|
simp1l |
|
30 |
29
|
hllatd |
|
31 |
|
simp2l |
|
32 |
|
simp1r |
|
33 |
1 6
|
lhpbase |
|
34 |
32 33
|
syl |
|
35 |
1 4
|
latmcl |
|
36 |
30 31 34 35
|
syl3anc |
|
37 |
1 2 4
|
latmle2 |
|
38 |
30 31 34 37
|
syl3anc |
|
39 |
1 2 6 18 16 20
|
diblss |
|
40 |
25 36 38 39
|
syl12anc |
|
41 |
6 18 19 20 21
|
dvhopellsm |
|
42 |
25 28 40 41
|
syl3anc |
|
43 |
|
vex |
|
44 |
|
vex |
|
45 |
2 5 6 7 8 10 17 12 43 44
|
dicopelval2 |
|
46 |
25 26 45
|
syl2anc |
|
47 |
1 2 6 8 9 15 16
|
dibopelval3 |
|
48 |
25 36 38 47
|
syl12anc |
|
49 |
46 48
|
anbi12d |
|
50 |
49
|
anbi1d |
|
51 |
|
simpl1 |
|
52 |
|
simprll |
|
53 |
|
simprlr |
|
54 |
2 5 6 7
|
lhpocnel2 |
|
55 |
51 54
|
syl |
|
56 |
|
simpl3l |
|
57 |
2 5 6 8 12
|
ltrniotacl |
|
58 |
51 55 56 57
|
syl3anc |
|
59 |
6 8 10
|
tendocl |
|
60 |
51 53 58 59
|
syl3anc |
|
61 |
52 60
|
eqeltrd |
|
62 |
|
simprll |
|
63 |
62
|
adantl |
|
64 |
|
simprrr |
|
65 |
1 6 8 10 15
|
tendo0cl |
|
66 |
51 65
|
syl |
|
67 |
64 66
|
eqeltrd |
|
68 |
|
eqid |
|
69 |
|
eqid |
|
70 |
6 8 10 18 68 19 69
|
dvhopvadd |
|
71 |
51 61 53 63 67 70
|
syl122anc |
|
72 |
6 8 10 18 68 22 69
|
dvhfplusr |
|
73 |
51 72
|
syl |
|
74 |
73
|
oveqd |
|
75 |
74
|
opeq2d |
|
76 |
71 75
|
eqtrd |
|
77 |
76
|
eqeq2d |
|
78 |
13 14
|
opth |
|
79 |
64
|
oveq2d |
|
80 |
1 6 8 10 15 22
|
tendo0plr |
|
81 |
51 53 80
|
syl2anc |
|
82 |
79 81
|
eqtrd |
|
83 |
82
|
eqeq2d |
|
84 |
83
|
anbi2d |
|
85 |
78 84
|
syl5bb |
|
86 |
77 85
|
bitrd |
|
87 |
86
|
pm5.32da |
|
88 |
|
simplll |
|
89 |
88
|
adantl |
|
90 |
|
simprrr |
|
91 |
90
|
fveq1d |
|
92 |
89 91
|
eqtr4d |
|
93 |
90
|
eqcomd |
|
94 |
|
coass |
|
95 |
|
simpl1 |
|
96 |
|
simpllr |
|
97 |
96
|
adantl |
|
98 |
90 97
|
eqeltrd |
|
99 |
58
|
adantrr |
|
100 |
6 8 10
|
tendocl |
|
101 |
95 98 99 100
|
syl3anc |
|
102 |
1 6 8
|
ltrn1o |
|
103 |
95 101 102
|
syl2anc |
|
104 |
|
f1ococnv1 |
|
105 |
103 104
|
syl |
|
106 |
105
|
coeq1d |
|
107 |
62
|
ad2antrl |
|
108 |
1 6 8
|
ltrn1o |
|
109 |
95 107 108
|
syl2anc |
|
110 |
|
f1of |
|
111 |
|
fcoi2 |
|
112 |
109 110 111
|
3syl |
|
113 |
106 112
|
eqtr2d |
|
114 |
|
simprrl |
|
115 |
92
|
coeq1d |
|
116 |
114 115
|
eqtrd |
|
117 |
116
|
coeq1d |
|
118 |
6 8
|
ltrncnv |
|
119 |
95 101 118
|
syl2anc |
|
120 |
6 8
|
ltrnco |
|
121 |
95 101 107 120
|
syl3anc |
|
122 |
6 8
|
ltrncom |
|
123 |
95 119 121 122
|
syl3anc |
|
124 |
117 123
|
eqtr4d |
|
125 |
94 113 124
|
3eqtr4a |
|
126 |
|
simplrr |
|
127 |
126
|
adantl |
|
128 |
125 127
|
jca |
|
129 |
92 93 128
|
jca31 |
|
130 |
129
|
ex |
|
131 |
130
|
pm4.71rd |
|
132 |
87 131
|
bitrd |
|
133 |
|
simprrl |
|
134 |
|
simpll1 |
|
135 |
88
|
adantl |
|
136 |
96
|
adantl |
|
137 |
134 54
|
syl |
|
138 |
|
simpl3l |
|
139 |
138
|
adantr |
|
140 |
134 137 139 57
|
syl3anc |
|
141 |
134 136 140 59
|
syl3anc |
|
142 |
135 141
|
eqeltrd |
|
143 |
62
|
ad2antrl |
|
144 |
6 8
|
ltrnco |
|
145 |
134 142 143 144
|
syl3anc |
|
146 |
133 145
|
eqeltrd |
|
147 |
|
simpl1l |
|
148 |
147
|
adantr |
|
149 |
148
|
hllatd |
|
150 |
1 6 8 9
|
trlcl |
|
151 |
134 143 150
|
syl2anc |
|
152 |
|
simpl2l |
|
153 |
152
|
adantr |
|
154 |
|
simpl1r |
|
155 |
154
|
adantr |
|
156 |
155 33
|
syl |
|
157 |
149 153 156 35
|
syl3anc |
|
158 |
|
simprlr |
|
159 |
158
|
ad2antrl |
|
160 |
1 2 4
|
latmle1 |
|
161 |
149 153 156 160
|
syl3anc |
|
162 |
1 2 149 151 157 153 159 161
|
lattrd |
|
163 |
146 136 162
|
jca31 |
|
164 |
|
simprll |
|
165 |
164
|
adantr |
|
166 |
|
simprlr |
|
167 |
166
|
adantr |
|
168 |
167
|
fveq1d |
|
169 |
165 168
|
eqtr4d |
|
170 |
|
simprlr |
|
171 |
169 170
|
jca |
|
172 |
|
simprrl |
|
173 |
172
|
adantr |
|
174 |
|
simpll1 |
|
175 |
|
simprll |
|
176 |
167 170
|
eqeltrrd |
|
177 |
174 54
|
syl |
|
178 |
138
|
adantr |
|
179 |
174 177 178 57
|
syl3anc |
|
180 |
174 176 179 100
|
syl3anc |
|
181 |
174 180 118
|
syl2anc |
|
182 |
6 8
|
ltrnco |
|
183 |
174 175 181 182
|
syl3anc |
|
184 |
173 183
|
eqeltrd |
|
185 |
|
simprr |
|
186 |
2 6 8 9
|
trlle |
|
187 |
174 184 186
|
syl2anc |
|
188 |
147
|
adantr |
|
189 |
188
|
hllatd |
|
190 |
174 184 150
|
syl2anc |
|
191 |
152
|
adantr |
|
192 |
154
|
adantr |
|
193 |
192 33
|
syl |
|
194 |
1 2 4
|
latlem12 |
|
195 |
189 190 191 193 194
|
syl13anc |
|
196 |
185 187 195
|
mpbi2and |
|
197 |
|
simprrr |
|
198 |
197
|
adantr |
|
199 |
184 196 198
|
jca31 |
|
200 |
174 180 102
|
syl2anc |
|
201 |
200 104
|
syl |
|
202 |
201
|
coeq2d |
|
203 |
1 6 8
|
ltrn1o |
|
204 |
174 175 203
|
syl2anc |
|
205 |
|
f1of |
|
206 |
|
fcoi1 |
|
207 |
204 205 206
|
3syl |
|
208 |
202 207
|
eqtr2d |
|
209 |
|
coass |
|
210 |
208 209
|
eqtr4di |
|
211 |
6 8
|
ltrncom |
|
212 |
174 180 183 211
|
syl3anc |
|
213 |
210 212
|
eqtr4d |
|
214 |
165 173
|
coeq12d |
|
215 |
213 214
|
eqtr4d |
|
216 |
167
|
eqcomd |
|
217 |
215 216
|
jca |
|
218 |
171 199 217
|
jca31 |
|
219 |
163 218
|
impbida |
|
220 |
219
|
pm5.32da |
|
221 |
|
df-3an |
|
222 |
220 221
|
bitr4di |
|
223 |
50 132 222
|
3bitrd |
|
224 |
223
|
4exbidv |
|
225 |
|
fvex |
|
226 |
225
|
cnvex |
|
227 |
13 226
|
coex |
|
228 |
8
|
fvexi |
|
229 |
228
|
mptex |
|
230 |
15 229
|
eqeltri |
|
231 |
|
biidd |
|
232 |
|
eleq1 |
|
233 |
232
|
anbi2d |
|
234 |
233
|
anbi1d |
|
235 |
|
fveq2 |
|
236 |
235
|
breq1d |
|
237 |
236
|
anbi2d |
|
238 |
|
biidd |
|
239 |
225 14 227 230 231 234 237 238
|
ceqsex4v |
|
240 |
224 239
|
syl6bb |
|
241 |
24 42 240
|
3bitrd |
|