Step |
Hyp |
Ref |
Expression |
1 |
|
xrhmeo.f |
|
2 |
|
xrhmeo.g |
|
3 |
|
xrhmeo.j |
|
4 |
|
iccssxr |
|
5 |
|
xrltso |
|
6 |
|
soss |
|
7 |
4 5 6
|
mp2 |
|
8 |
|
sopo |
|
9 |
5 8
|
ax-mp |
|
10 |
|
iccssxr |
|
11 |
|
neg1rr |
|
12 |
|
1re |
|
13 |
11 12
|
elicc2i |
|
14 |
13
|
simp1bi |
|
15 |
14
|
adantr |
|
16 |
|
simpr |
|
17 |
13
|
simp3bi |
|
18 |
17
|
adantr |
|
19 |
|
elicc01 |
|
20 |
15 16 18 19
|
syl3anbrc |
|
21 |
1
|
iccpnfcnv |
|
22 |
21
|
simpli |
|
23 |
|
f1of |
|
24 |
22 23
|
ax-mp |
|
25 |
24
|
ffvelrni |
|
26 |
20 25
|
syl |
|
27 |
10 26
|
sseldi |
|
28 |
14
|
adantr |
|
29 |
28
|
renegcld |
|
30 |
|
0re |
|
31 |
|
letric |
|
32 |
30 14 31
|
sylancr |
|
33 |
32
|
orcanai |
|
34 |
28
|
le0neg1d |
|
35 |
33 34
|
mpbid |
|
36 |
13
|
simp2bi |
|
37 |
36
|
adantr |
|
38 |
|
lenegcon1 |
|
39 |
12 28 38
|
sylancr |
|
40 |
37 39
|
mpbid |
|
41 |
|
elicc01 |
|
42 |
29 35 40 41
|
syl3anbrc |
|
43 |
24
|
ffvelrni |
|
44 |
42 43
|
syl |
|
45 |
10 44
|
sseldi |
|
46 |
45
|
xnegcld |
|
47 |
27 46
|
ifclda |
|
48 |
2 47
|
fmpti |
|
49 |
|
frn |
|
50 |
48 49
|
ax-mp |
|
51 |
|
ssabral |
|
52 |
|
0le1 |
|
53 |
|
le0neg2 |
|
54 |
12 53
|
ax-mp |
|
55 |
52 54
|
mpbi |
|
56 |
|
1le1 |
|
57 |
|
iccss |
|
58 |
11 12 55 56 57
|
mp4an |
|
59 |
|
elxrge0 |
|
60 |
|
f1ocnv |
|
61 |
|
f1of |
|
62 |
22 60 61
|
mp2b |
|
63 |
62
|
ffvelrni |
|
64 |
59 63
|
sylbir |
|
65 |
58 64
|
sseldi |
|
66 |
|
elicc01 |
|
67 |
66
|
simp2bi |
|
68 |
64 67
|
syl |
|
69 |
59
|
biimpri |
|
70 |
|
f1ocnvfv2 |
|
71 |
22 69 70
|
sylancr |
|
72 |
71
|
eqcomd |
|
73 |
|
breq2 |
|
74 |
|
fveq2 |
|
75 |
74
|
eqeq2d |
|
76 |
73 75
|
anbi12d |
|
77 |
76
|
rspcev |
|
78 |
65 68 72 77
|
syl12anc |
|
79 |
|
iftrue |
|
80 |
79
|
eqeq2d |
|
81 |
80
|
biimpar |
|
82 |
81
|
reximi |
|
83 |
78 82
|
syl |
|
84 |
|
xnegcl |
|
85 |
84
|
adantr |
|
86 |
|
0xr |
|
87 |
|
xrletri |
|
88 |
86 87
|
mpan |
|
89 |
88
|
ord |
|
90 |
|
xle0neg1 |
|
91 |
89 90
|
sylibd |
|
92 |
91
|
imp |
|
93 |
|
elxrge0 |
|
94 |
85 92 93
|
sylanbrc |
|
95 |
62
|
ffvelrni |
|
96 |
94 95
|
syl |
|
97 |
58 96
|
sseldi |
|
98 |
|
iccssre |
|
99 |
11 12 98
|
mp2an |
|
100 |
99 97
|
sseldi |
|
101 |
|
iccneg |
|
102 |
11 12 101
|
mp3an12 |
|
103 |
100 102
|
syl |
|
104 |
97 103
|
mpbid |
|
105 |
|
negneg1e1 |
|
106 |
105
|
oveq2i |
|
107 |
104 106
|
eleqtrdi |
|
108 |
|
xle0neg2 |
|
109 |
108
|
notbid |
|
110 |
109
|
biimpa |
|
111 |
|
f1ocnvfv2 |
|
112 |
22 94 111
|
sylancr |
|
113 |
|
0elunit |
|
114 |
|
ax-1ne0 |
|
115 |
|
neeq2 |
|
116 |
114 115
|
mpbiri |
|
117 |
116
|
necomd |
|
118 |
|
ifnefalse |
|
119 |
117 118
|
syl |
|
120 |
|
id |
|
121 |
|
oveq2 |
|
122 |
|
1m0e1 |
|
123 |
121 122
|
eqtrdi |
|
124 |
120 123
|
oveq12d |
|
125 |
|
ax-1cn |
|
126 |
125 114
|
div0i |
|
127 |
124 126
|
eqtrdi |
|
128 |
119 127
|
eqtrd |
|
129 |
|
c0ex |
|
130 |
128 1 129
|
fvmpt |
|
131 |
113 130
|
ax-mp |
|
132 |
131
|
a1i |
|
133 |
112 132
|
breq12d |
|
134 |
110 133
|
mtbird |
|
135 |
|
eqid |
|
136 |
1 135
|
iccpnfhmeo |
|
137 |
136
|
simpli |
|
138 |
|
iccssxr |
|
139 |
138 10
|
pm3.2i |
|
140 |
|
leisorel |
|
141 |
137 139 140
|
mp3an12 |
|
142 |
96 113 141
|
sylancl |
|
143 |
134 142
|
mtbird |
|
144 |
100
|
le0neg1d |
|
145 |
143 144
|
mtbid |
|
146 |
|
unitssre |
|
147 |
146 96
|
sseldi |
|
148 |
147
|
recnd |
|
149 |
148
|
negnegd |
|
150 |
149
|
fveq2d |
|
151 |
150 112
|
eqtrd |
|
152 |
|
xnegeq |
|
153 |
151 152
|
syl |
|
154 |
|
xnegneg |
|
155 |
154
|
adantr |
|
156 |
153 155
|
eqtr2d |
|
157 |
|
breq2 |
|
158 |
157
|
notbid |
|
159 |
|
negeq |
|
160 |
159
|
fveq2d |
|
161 |
|
xnegeq |
|
162 |
160 161
|
syl |
|
163 |
162
|
eqeq2d |
|
164 |
158 163
|
anbi12d |
|
165 |
164
|
rspcev |
|
166 |
107 145 156 165
|
syl12anc |
|
167 |
|
iffalse |
|
168 |
167
|
eqeq2d |
|
169 |
168
|
biimpar |
|
170 |
169
|
reximi |
|
171 |
166 170
|
syl |
|
172 |
83 171
|
pm2.61dan |
|
173 |
51 172
|
mprgbir |
|
174 |
2
|
rnmpt |
|
175 |
173 174
|
sseqtrri |
|
176 |
50 175
|
eqssi |
|
177 |
|
dffo2 |
|
178 |
48 176 177
|
mpbir2an |
|
179 |
|
breq1 |
|
180 |
|
breq1 |
|
181 |
|
simpl3 |
|
182 |
|
simpl1 |
|
183 |
|
simpr |
|
184 |
|
breq2 |
|
185 |
|
eleq1w |
|
186 |
184 185
|
imbi12d |
|
187 |
20
|
ex |
|
188 |
186 187
|
vtoclga |
|
189 |
182 183 188
|
sylc |
|
190 |
|
simpl2 |
|
191 |
30
|
a1i |
|
192 |
99 182
|
sseldi |
|
193 |
99 190
|
sseldi |
|
194 |
192 193 181
|
ltled |
|
195 |
191 192 193 183 194
|
letrd |
|
196 |
|
breq2 |
|
197 |
|
eleq1w |
|
198 |
196 197
|
imbi12d |
|
199 |
198 187
|
vtoclga |
|
200 |
190 195 199
|
sylc |
|
201 |
|
isorel |
|
202 |
137 201
|
mpan |
|
203 |
189 200 202
|
syl2anc |
|
204 |
181 203
|
mpbid |
|
205 |
195
|
iftrued |
|
206 |
204 205
|
breqtrrd |
|
207 |
|
breq2 |
|
208 |
|
breq2 |
|
209 |
|
simpl1 |
|
210 |
|
simpr |
|
211 |
184
|
notbid |
|
212 |
|
negeq |
|
213 |
212
|
eleq1d |
|
214 |
211 213
|
imbi12d |
|
215 |
42
|
ex |
|
216 |
214 215
|
vtoclga |
|
217 |
209 210 216
|
sylc |
|
218 |
217
|
adantr |
|
219 |
24
|
ffvelrni |
|
220 |
218 219
|
syl |
|
221 |
10 220
|
sseldi |
|
222 |
221
|
xnegcld |
|
223 |
86
|
a1i |
|
224 |
|
simpll2 |
|
225 |
|
simpr |
|
226 |
224 225 199
|
sylc |
|
227 |
24
|
ffvelrni |
|
228 |
226 227
|
syl |
|
229 |
10 228
|
sseldi |
|
230 |
210
|
adantr |
|
231 |
|
simpll1 |
|
232 |
99 231
|
sseldi |
|
233 |
|
ltnle |
|
234 |
232 30 233
|
sylancl |
|
235 |
230 234
|
mpbird |
|
236 |
232
|
lt0neg1d |
|
237 |
235 236
|
mpbid |
|
238 |
|
isorel |
|
239 |
137 238
|
mpan |
|
240 |
113 218 239
|
sylancr |
|
241 |
237 240
|
mpbid |
|
242 |
131 241
|
eqbrtrrid |
|
243 |
|
xlt0neg2 |
|
244 |
221 243
|
syl |
|
245 |
242 244
|
mpbid |
|
246 |
|
elxrge0 |
|
247 |
246
|
simprbi |
|
248 |
228 247
|
syl |
|
249 |
222 223 229 245 248
|
xrltletrd |
|
250 |
|
simpll3 |
|
251 |
|
simpll1 |
|
252 |
99 251
|
sseldi |
|
253 |
|
simpll2 |
|
254 |
99 253
|
sseldi |
|
255 |
252 254
|
ltnegd |
|
256 |
250 255
|
mpbid |
|
257 |
|
simpr |
|
258 |
196
|
notbid |
|
259 |
|
negeq |
|
260 |
259
|
eleq1d |
|
261 |
258 260
|
imbi12d |
|
262 |
261 215
|
vtoclga |
|
263 |
253 257 262
|
sylc |
|
264 |
217
|
adantr |
|
265 |
|
isorel |
|
266 |
137 265
|
mpan |
|
267 |
263 264 266
|
syl2anc |
|
268 |
256 267
|
mpbid |
|
269 |
24
|
ffvelrni |
|
270 |
263 269
|
syl |
|
271 |
10 270
|
sseldi |
|
272 |
264 219
|
syl |
|
273 |
10 272
|
sseldi |
|
274 |
|
xltneg |
|
275 |
271 273 274
|
syl2anc |
|
276 |
268 275
|
mpbid |
|
277 |
207 208 249 276
|
ifbothda |
|
278 |
179 180 206 277
|
ifbothda |
|
279 |
278
|
3expia |
|
280 |
|
fveq2 |
|
281 |
212
|
fveq2d |
|
282 |
|
xnegeq |
|
283 |
281 282
|
syl |
|
284 |
184 280 283
|
ifbieq12d |
|
285 |
|
fvex |
|
286 |
|
xnegex |
|
287 |
285 286
|
ifex |
|
288 |
284 2 287
|
fvmpt |
|
289 |
|
fveq2 |
|
290 |
259
|
fveq2d |
|
291 |
|
xnegeq |
|
292 |
290 291
|
syl |
|
293 |
196 289 292
|
ifbieq12d |
|
294 |
|
fvex |
|
295 |
|
xnegex |
|
296 |
294 295
|
ifex |
|
297 |
293 2 296
|
fvmpt |
|
298 |
288 297
|
breqan12d |
|
299 |
279 298
|
sylibrd |
|
300 |
299
|
rgen2 |
|
301 |
|
soisoi |
|
302 |
7 9 178 300 301
|
mp4an |
|
303 |
|
letsr |
|
304 |
303
|
elexi |
|
305 |
304
|
inex1 |
|
306 |
|
ssid |
|
307 |
|
leiso |
|
308 |
4 306 307
|
mp2an |
|
309 |
302 308
|
mpbi |
|
310 |
|
isores1 |
|
311 |
309 310
|
mpbi |
|
312 |
|
tsrps |
|
313 |
303 312
|
ax-mp |
|
314 |
|
ledm |
|
315 |
314
|
psssdm |
|
316 |
313 4 315
|
mp2an |
|
317 |
316
|
eqcomi |
|
318 |
317 314
|
ordthmeo |
|
319 |
305 303 311 318
|
mp3an |
|
320 |
|
eqid |
|
321 |
3 320
|
xrrest2 |
|
322 |
99 321
|
ax-mp |
|
323 |
|
ordtresticc |
|
324 |
322 323
|
eqtri |
|
325 |
324
|
oveq1i |
|
326 |
319 325
|
eleqtrri |
|
327 |
302 326
|
pm3.2i |
|