| Step |
Hyp |
Ref |
Expression |
| 1 |
|
sge0f1o.1 |
|
| 2 |
|
sge0f1o.2 |
|
| 3 |
|
sge0f1o.3 |
|
| 4 |
|
sge0f1o.4 |
|
| 5 |
|
sge0f1o.5 |
|
| 6 |
|
sge0f1o.6 |
|
| 7 |
|
sge0f1o.7 |
|
| 8 |
|
f1ofo |
|
| 9 |
5 8
|
syl |
|
| 10 |
|
focdmex |
|
| 11 |
4 9 10
|
sylc |
|
| 12 |
11
|
adantr |
|
| 13 |
1 7
|
fmptd2f |
|
| 14 |
13
|
adantr |
|
| 15 |
|
nfv |
|
| 16 |
|
simp3 |
|
| 17 |
|
f1of |
|
| 18 |
5 17
|
syl |
|
| 19 |
18
|
ffvelcdmda |
|
| 20 |
|
nfv |
|
| 21 |
|
nfcsb1v |
|
| 22 |
21
|
nfeq1 |
|
| 23 |
20 22
|
nfim |
|
| 24 |
|
eqeq1 |
|
| 25 |
|
csbeq1a |
|
| 26 |
25
|
eqeq1d |
|
| 27 |
24 26
|
imbi12d |
|
| 28 |
23 27 3
|
vtoclg1f |
|
| 29 |
19 6 28
|
sylc |
|
| 30 |
29
|
eqcomd |
|
| 31 |
30
|
3adant3 |
|
| 32 |
16 31
|
eqtrd |
|
| 33 |
|
simpl |
|
| 34 |
33 19
|
jca |
|
| 35 |
|
nfv |
|
| 36 |
1 35
|
nfan |
|
| 37 |
21
|
nfel1 |
|
| 38 |
36 37
|
nfim |
|
| 39 |
|
eleq1 |
|
| 40 |
39
|
anbi2d |
|
| 41 |
25
|
eleq1d |
|
| 42 |
40 41
|
imbi12d |
|
| 43 |
38 42 7
|
vtoclg1f |
|
| 44 |
19 34 43
|
sylc |
|
| 45 |
|
eqid |
|
| 46 |
21 45 25
|
elrnmpt1sf |
|
| 47 |
19 44 46
|
syl2anc |
|
| 48 |
47
|
3adant3 |
|
| 49 |
32 48
|
eqeltrd |
|
| 50 |
49
|
3exp |
|
| 51 |
2 15 50
|
rexlimd |
|
| 52 |
|
pnfex |
|
| 53 |
|
eqid |
|
| 54 |
53
|
elrnmpt |
|
| 55 |
52 54
|
ax-mp |
|
| 56 |
55
|
biimpi |
|
| 57 |
51 56
|
impel |
|
| 58 |
12 14 57
|
sge0pnfval |
|
| 59 |
4
|
adantr |
|
| 60 |
30 44
|
eqeltrd |
|
| 61 |
2 60
|
fmptd2f |
|
| 62 |
61
|
adantr |
|
| 63 |
|
simpr |
|
| 64 |
59 62 63
|
sge0pnfval |
|
| 65 |
58 64
|
eqtr4d |
|
| 66 |
|
sumex |
|
| 67 |
66
|
a1i |
|
| 68 |
|
cnvimass |
|
| 69 |
68 18
|
fssdm |
|
| 70 |
4 69
|
sselpwd |
|
| 71 |
70
|
adantr |
|
| 72 |
|
f1ocnv |
|
| 73 |
5 72
|
syl |
|
| 74 |
|
f1ofun |
|
| 75 |
73 74
|
syl |
|
| 76 |
|
elinel2 |
|
| 77 |
|
imafi |
|
| 78 |
75 76 77
|
syl2an |
|
| 79 |
71 78
|
elind |
|
| 80 |
79
|
adantlr |
|
| 81 |
|
nfv |
|
| 82 |
1 81
|
nfan |
|
| 83 |
|
nfv |
|
| 84 |
82 83
|
nfan |
|
| 85 |
|
nfmpt1 |
|
| 86 |
85
|
nfrn |
|
| 87 |
86
|
nfel2 |
|
| 88 |
87
|
nfn |
|
| 89 |
2 88
|
nfan |
|
| 90 |
|
nfv |
|
| 91 |
89 90
|
nfan |
|
| 92 |
78
|
adantlr |
|
| 93 |
|
f1of1 |
|
| 94 |
5 93
|
syl |
|
| 95 |
94
|
adantr |
|
| 96 |
69
|
adantr |
|
| 97 |
|
f1ores |
|
| 98 |
95 96 97
|
syl2anc |
|
| 99 |
|
elpwinss |
|
| 100 |
|
foimacnv |
|
| 101 |
9 99 100
|
syl2an |
|
| 102 |
101
|
f1oeq3d |
|
| 103 |
98 102
|
mpbid |
|
| 104 |
103
|
adantlr |
|
| 105 |
18 4
|
fexd |
|
| 106 |
|
cnvexg |
|
| 107 |
105 106
|
syl |
|
| 108 |
107
|
imaexd |
|
| 109 |
108
|
ad2antrr |
|
| 110 |
|
simpll |
|
| 111 |
79
|
adantr |
|
| 112 |
|
simpr |
|
| 113 |
110 111 112
|
jca31 |
|
| 114 |
|
eleq1 |
|
| 115 |
114
|
anbi2d |
|
| 116 |
|
eleq2w2 |
|
| 117 |
115 116
|
anbi12d |
|
| 118 |
|
reseq2 |
|
| 119 |
118
|
fveq1d |
|
| 120 |
119
|
eqeq1d |
|
| 121 |
117 120
|
imbi12d |
|
| 122 |
|
fvres |
|
| 123 |
122
|
adantl |
|
| 124 |
|
simpll |
|
| 125 |
|
elpwinss |
|
| 126 |
125
|
adantl |
|
| 127 |
126
|
sselda |
|
| 128 |
124 127 6
|
syl2anc |
|
| 129 |
123 128
|
eqtrd |
|
| 130 |
121 129
|
vtoclg |
|
| 131 |
109 113 130
|
sylc |
|
| 132 |
131
|
adantllr |
|
| 133 |
108
|
ad3antrrr |
|
| 134 |
|
simpll |
|
| 135 |
70
|
ad3antrrr |
|
| 136 |
92
|
adantr |
|
| 137 |
135 136
|
elind |
|
| 138 |
|
simpr |
|
| 139 |
101
|
eqcomd |
|
| 140 |
139
|
adantr |
|
| 141 |
138 140
|
eleqtrd |
|
| 142 |
141
|
adantllr |
|
| 143 |
134 137 142
|
jca31 |
|
| 144 |
114
|
anbi2d |
|
| 145 |
|
imaeq2 |
|
| 146 |
145
|
eleq2d |
|
| 147 |
144 146
|
anbi12d |
|
| 148 |
147
|
imbi1d |
|
| 149 |
|
rge0ssre |
|
| 150 |
|
ax-resscn |
|
| 151 |
149 150
|
sstri |
|
| 152 |
|
simplll |
|
| 153 |
|
simpllr |
|
| 154 |
18
|
fimassd |
|
| 155 |
154
|
ad2antrr |
|
| 156 |
|
simpr |
|
| 157 |
155 156
|
sseldd |
|
| 158 |
157
|
adantllr |
|
| 159 |
|
foelcdmi |
|
| 160 |
9 159
|
sylan |
|
| 161 |
160
|
adantlr |
|
| 162 |
|
nfv |
|
| 163 |
89 162
|
nfan |
|
| 164 |
|
nfv |
|
| 165 |
|
csbid |
|
| 166 |
165
|
eqcomi |
|
| 167 |
166
|
a1i |
|
| 168 |
|
id |
|
| 169 |
168
|
eqcomd |
|
| 170 |
169
|
csbeq1d |
|
| 171 |
170
|
3ad2ant3 |
|
| 172 |
29
|
3adant3 |
|
| 173 |
167 171 172
|
3eqtrd |
|
| 174 |
173
|
3adant1r |
|
| 175 |
|
0xr |
|
| 176 |
175
|
a1i |
|
| 177 |
|
pnfxr |
|
| 178 |
177
|
a1i |
|
| 179 |
60
|
adantr |
|
| 180 |
|
simpr |
|
| 181 |
176 178 179 180
|
eliccnelico |
|
| 182 |
181
|
eqcomd |
|
| 183 |
|
simpr |
|
| 184 |
53 183 60
|
elrnmpt1d |
|
| 185 |
184
|
adantr |
|
| 186 |
182 185
|
eqeltrd |
|
| 187 |
186
|
adantllr |
|
| 188 |
|
simpllr |
|
| 189 |
187 188
|
condan |
|
| 190 |
189
|
3adant3 |
|
| 191 |
174 190
|
eqeltrd |
|
| 192 |
191
|
3exp |
|
| 193 |
192
|
adantr |
|
| 194 |
163 164 193
|
rexlimd |
|
| 195 |
161 194
|
mpd |
|
| 196 |
152 153 158 195
|
syl21anc |
|
| 197 |
151 196
|
sselid |
|
| 198 |
148 197
|
vtoclg |
|
| 199 |
133 143 198
|
sylc |
|
| 200 |
84 91 3 92 104 132 199
|
fsumf1of |
|
| 201 |
|
sumeq1 |
|
| 202 |
201
|
rspceeqv |
|
| 203 |
80 200 202
|
syl2anc |
|
| 204 |
67 203
|
rnmptssrn |
|
| 205 |
|
sumex |
|
| 206 |
205
|
a1i |
|
| 207 |
11 154
|
sselpwd |
|
| 208 |
207
|
adantr |
|
| 209 |
18
|
ffund |
|
| 210 |
|
elinel2 |
|
| 211 |
|
imafi |
|
| 212 |
209 210 211
|
syl2an |
|
| 213 |
208 212
|
elind |
|
| 214 |
213
|
adantlr |
|
| 215 |
|
nfv |
|
| 216 |
82 215
|
nfan |
|
| 217 |
|
nfv |
|
| 218 |
89 217
|
nfan |
|
| 219 |
210
|
adantl |
|
| 220 |
|
f1ores |
|
| 221 |
94 125 220
|
syl2an |
|
| 222 |
221
|
adantlr |
|
| 223 |
129
|
adantllr |
|
| 224 |
216 218 3 219 222 223 197
|
fsumf1of |
|
| 225 |
224
|
eqcomd |
|
| 226 |
|
sumeq1 |
|
| 227 |
226
|
rspceeqv |
|
| 228 |
214 225 227
|
syl2anc |
|
| 229 |
206 228
|
rnmptssrn |
|
| 230 |
204 229
|
eqssd |
|
| 231 |
230
|
supeq1d |
|
| 232 |
11
|
adantr |
|
| 233 |
82 232 195
|
sge0revalmpt |
|
| 234 |
4
|
adantr |
|
| 235 |
89 234 189
|
sge0revalmpt |
|
| 236 |
231 233 235
|
3eqtr4d |
|
| 237 |
65 236
|
pm2.61dan |
|