Step |
Hyp |
Ref |
Expression |
1 |
|
lhop1.a |
|
2 |
|
lhop1.b |
|
3 |
|
lhop1.l |
|
4 |
|
lhop1.f |
|
5 |
|
lhop1.g |
|
6 |
|
lhop1.if |
|
7 |
|
lhop1.ig |
|
8 |
|
lhop1.f0 |
|
9 |
|
lhop1.g0 |
|
10 |
|
lhop1.gn0 |
|
11 |
|
lhop1.gd0 |
|
12 |
|
lhop1.c |
|
13 |
|
simpr |
|
14 |
13
|
rphalfcld |
|
15 |
|
breq2 |
|
16 |
15
|
imbi2d |
|
17 |
16
|
rexralbidv |
|
18 |
17
|
rspcv |
|
19 |
14 18
|
syl |
|
20 |
|
rabid |
|
21 |
|
eliooord |
|
22 |
21
|
adantl |
|
23 |
22
|
simprd |
|
24 |
23
|
biantrurd |
|
25 |
|
ioossre |
|
26 |
|
simpr |
|
27 |
25 26
|
sselid |
|
28 |
1
|
ad3antrrr |
|
29 |
|
simpr |
|
30 |
29
|
rpred |
|
31 |
30
|
adantr |
|
32 |
27 28 31
|
ltsubaddd |
|
33 |
27
|
rexrd |
|
34 |
2
|
ad3antrrr |
|
35 |
1
|
ad2antrr |
|
36 |
30 35
|
readdcld |
|
37 |
36
|
rexrd |
|
38 |
37
|
adantr |
|
39 |
|
xrltmin |
|
40 |
33 34 38 39
|
syl3anc |
|
41 |
24 32 40
|
3bitr4rd |
|
42 |
28
|
rexrd |
|
43 |
34 38
|
ifcld |
|
44 |
22
|
simpld |
|
45 |
|
elioo5 |
|
46 |
45
|
baibd |
|
47 |
42 43 33 44 46
|
syl31anc |
|
48 |
28 27 44
|
ltled |
|
49 |
28 27 48
|
abssubge0d |
|
50 |
49
|
breq1d |
|
51 |
41 47 50
|
3bitr4d |
|
52 |
51
|
rabbi2dva |
|
53 |
2
|
ad2antrr |
|
54 |
|
xrmin1 |
|
55 |
53 37 54
|
syl2anc |
|
56 |
|
iooss2 |
|
57 |
53 55 56
|
syl2anc |
|
58 |
|
sseqin2 |
|
59 |
57 58
|
sylib |
|
60 |
52 59
|
eqtr3d |
|
61 |
60
|
eleq2d |
|
62 |
20 61
|
bitr3id |
|
63 |
|
lbioo |
|
64 |
|
eleq1 |
|
65 |
63 64
|
mtbiri |
|
66 |
65
|
necon2ai |
|
67 |
66
|
biantrurd |
|
68 |
67
|
bicomd |
|
69 |
|
fveq2 |
|
70 |
|
fveq2 |
|
71 |
69 70
|
oveq12d |
|
72 |
|
eqid |
|
73 |
|
ovex |
|
74 |
71 72 73
|
fvmpt3i |
|
75 |
74
|
fvoveq1d |
|
76 |
75
|
breq1d |
|
77 |
68 76
|
imbi12d |
|
78 |
77
|
ralbiia |
|
79 |
|
fvoveq1 |
|
80 |
79
|
breq1d |
|
81 |
80
|
ralrab |
|
82 |
78 81
|
bitr4i |
|
83 |
60
|
adantrr |
|
84 |
83
|
raleqdv |
|
85 |
1
|
ad2antrr |
|
86 |
2
|
ad2antrr |
|
87 |
3
|
ad2antrr |
|
88 |
4
|
ad2antrr |
|
89 |
5
|
ad2antrr |
|
90 |
6
|
ad2antrr |
|
91 |
7
|
ad2antrr |
|
92 |
8
|
ad2antrr |
|
93 |
9
|
ad2antrr |
|
94 |
10
|
ad2antrr |
|
95 |
11
|
ad2antrr |
|
96 |
12
|
ad2antrr |
|
97 |
14
|
adantr |
|
98 |
85
|
rexrd |
|
99 |
|
simprll |
|
100 |
99
|
rpred |
|
101 |
100 85
|
readdcld |
|
102 |
|
iocssre |
|
103 |
98 101 102
|
syl2anc |
|
104 |
86
|
adantr |
|
105 |
100
|
adantr |
|
106 |
85
|
adantr |
|
107 |
105 106
|
readdcld |
|
108 |
107
|
rexrd |
|
109 |
104 108
|
ifclda |
|
110 |
85 99
|
ltaddrp2d |
|
111 |
101
|
rexrd |
|
112 |
|
xrltmin |
|
113 |
98 86 111 112
|
syl3anc |
|
114 |
87 110 113
|
mpbir2and |
|
115 |
|
xrmin2 |
|
116 |
86 111 115
|
syl2anc |
|
117 |
|
elioc1 |
|
118 |
98 111 117
|
syl2anc |
|
119 |
109 114 116 118
|
mpbir3and |
|
120 |
103 119
|
sseldd |
|
121 |
86 111 54
|
syl2anc |
|
122 |
|
simprlr |
|
123 |
|
simprr |
|
124 |
|
eqid |
|
125 |
85 86 87 88 89 90 91 92 93 94 95 96 97 120 121 122 123 124
|
lhop1lem |
|
126 |
13
|
rpcnd |
|
127 |
|
2cnd |
|
128 |
|
2ne0 |
|
129 |
128
|
a1i |
|
130 |
126 127 129
|
divcan2d |
|
131 |
130
|
adantr |
|
132 |
125 131
|
breqtrd |
|
133 |
132
|
expr |
|
134 |
84 133
|
sylbid |
|
135 |
82 134
|
syl5bi |
|
136 |
135
|
expr |
|
137 |
62 136
|
sylbid |
|
138 |
137
|
expdimp |
|
139 |
|
fveq2 |
|
140 |
|
fveq2 |
|
141 |
139 140
|
oveq12d |
|
142 |
|
eqid |
|
143 |
|
ovex |
|
144 |
141 142 143
|
fvmpt3i |
|
145 |
144
|
fvoveq1d |
|
146 |
145
|
breq1d |
|
147 |
146
|
imbi2d |
|
148 |
147
|
adantl |
|
149 |
138 148
|
sylibrd |
|
150 |
149
|
adantld |
|
151 |
150
|
com23 |
|
152 |
151
|
ralrimdva |
|
153 |
152
|
reximdva |
|
154 |
19 153
|
syld |
|
155 |
154
|
ralrimdva |
|
156 |
155
|
anim2d |
|
157 |
|
dvf |
|
158 |
6
|
feq2d |
|
159 |
157 158
|
mpbii |
|
160 |
159
|
ffvelrnda |
|
161 |
|
dvf |
|
162 |
7
|
feq2d |
|
163 |
161 162
|
mpbii |
|
164 |
163
|
ffvelrnda |
|
165 |
11
|
adantr |
|
166 |
163
|
ffnd |
|
167 |
|
fnfvelrn |
|
168 |
166 167
|
sylan |
|
169 |
|
eleq1 |
|
170 |
168 169
|
syl5ibcom |
|
171 |
170
|
necon3bd |
|
172 |
165 171
|
mpd |
|
173 |
160 164 172
|
divcld |
|
174 |
173
|
fmpttd |
|
175 |
|
ax-resscn |
|
176 |
25 175
|
sstri |
|
177 |
176
|
a1i |
|
178 |
1
|
recnd |
|
179 |
174 177 178
|
ellimc3 |
|
180 |
4
|
ffvelrnda |
|
181 |
180
|
recnd |
|
182 |
5
|
ffvelrnda |
|
183 |
182
|
recnd |
|
184 |
10
|
adantr |
|
185 |
5
|
ffnd |
|
186 |
|
fnfvelrn |
|
187 |
185 186
|
sylan |
|
188 |
|
eleq1 |
|
189 |
187 188
|
syl5ibcom |
|
190 |
189
|
necon3bd |
|
191 |
184 190
|
mpd |
|
192 |
181 183 191
|
divcld |
|
193 |
192
|
fmpttd |
|
194 |
193 177 178
|
ellimc3 |
|
195 |
156 179 194
|
3imtr4d |
|
196 |
12 195
|
mpd |
|