Step |
Hyp |
Ref |
Expression |
1 |
|
jm2.27a1 |
|
2 |
|
jm2.27a2 |
|
3 |
|
jm2.27a3 |
|
4 |
|
jm2.27c4 |
|
5 |
|
jm2.27c5 |
|
6 |
|
jm2.27c6 |
|
7 |
|
jm2.27c7 |
|
8 |
|
jm2.27c8 |
|
9 |
|
jm2.27c9 |
|
10 |
|
jm2.27c10 |
|
11 |
|
jm2.27c11 |
|
12 |
|
jm2.27c12 |
|
13 |
2
|
nnzd |
|
14 |
|
frmx |
|
15 |
14
|
fovcl |
|
16 |
1 13 15
|
syl2anc |
|
17 |
5 16
|
eqeltrid |
|
18 |
|
2z |
|
19 |
3
|
nnzd |
|
20 |
4 19
|
eqeltrrd |
|
21 |
13 20
|
zmulcld |
|
22 |
6 21
|
eqeltrid |
|
23 |
|
zmulcl |
|
24 |
18 22 23
|
sylancr |
|
25 |
|
frmy |
|
26 |
25
|
fovcl |
|
27 |
1 24 26
|
syl2anc |
|
28 |
|
rmy0 |
|
29 |
1 28
|
syl |
|
30 |
|
2nn |
|
31 |
4 3
|
eqeltrrd |
|
32 |
2 31
|
nnmulcld |
|
33 |
6 32
|
eqeltrid |
|
34 |
|
nnmulcl |
|
35 |
30 33 34
|
sylancr |
|
36 |
35
|
nnnn0d |
|
37 |
36
|
nn0ge0d |
|
38 |
|
0zd |
|
39 |
|
lermy |
|
40 |
1 38 24 39
|
syl3anc |
|
41 |
37 40
|
mpbid |
|
42 |
29 41
|
eqbrtrrd |
|
43 |
|
elnn0z |
|
44 |
27 42 43
|
sylanbrc |
|
45 |
7 44
|
eqeltrid |
|
46 |
14
|
fovcl |
|
47 |
1 24 46
|
syl2anc |
|
48 |
8 47
|
eqeltrid |
|
49 |
17 45 48
|
3jca |
|
50 |
|
2nn0 |
|
51 |
48
|
nn0cnd |
|
52 |
51
|
sqvald |
|
53 |
48 48
|
nn0mulcld |
|
54 |
52 53
|
eqeltrd |
|
55 |
|
eluz2nn |
|
56 |
1 55
|
syl |
|
57 |
56
|
nnnn0d |
|
58 |
57
|
nn0red |
|
59 |
48
|
nn0red |
|
60 |
59 59
|
remulcld |
|
61 |
|
rmx1 |
|
62 |
1 61
|
syl |
|
63 |
35
|
nnge1d |
|
64 |
|
1nn0 |
|
65 |
64
|
a1i |
|
66 |
|
lermxnn0 |
|
67 |
1 65 36 66
|
syl3anc |
|
68 |
63 67
|
mpbid |
|
69 |
62 68
|
eqbrtrrd |
|
70 |
69 8
|
breqtrrdi |
|
71 |
48
|
nn0ge0d |
|
72 |
|
rmxnn |
|
73 |
1 24 72
|
syl2anc |
|
74 |
8 73
|
eqeltrid |
|
75 |
74
|
nnge1d |
|
76 |
59 59 71 75
|
lemulge12d |
|
77 |
58 59 60 70 76
|
letrd |
|
78 |
77 52
|
breqtrrd |
|
79 |
|
nn0sub |
|
80 |
57 54 79
|
syl2anc |
|
81 |
78 80
|
mpbid |
|
82 |
54 81
|
nn0mulcld |
|
83 |
|
uzaddcl |
|
84 |
1 82 83
|
syl2anc |
|
85 |
9 84
|
eqeltrid |
|
86 |
|
eluznn0 |
|
87 |
50 85 86
|
sylancr |
|
88 |
25
|
fovcl |
|
89 |
85 13 88
|
syl2anc |
|
90 |
|
rmy0 |
|
91 |
85 90
|
syl |
|
92 |
2
|
nnnn0d |
|
93 |
92
|
nn0ge0d |
|
94 |
|
lermy |
|
95 |
85 38 13 94
|
syl3anc |
|
96 |
93 95
|
mpbid |
|
97 |
91 96
|
eqbrtrrd |
|
98 |
|
elnn0z |
|
99 |
89 97 98
|
sylanbrc |
|
100 |
10 99
|
eqeltrid |
|
101 |
14
|
fovcl |
|
102 |
85 13 101
|
syl2anc |
|
103 |
11 102
|
eqeltrid |
|
104 |
87 100 103
|
3jca |
|
105 |
|
zsqcl |
|
106 |
20 105
|
syl |
|
107 |
|
zmulcl |
|
108 |
18 106 107
|
sylancr |
|
109 |
25
|
fovcl |
|
110 |
1 22 109
|
syl2anc |
|
111 |
|
zmulcl |
|
112 |
18 110 111
|
sylancr |
|
113 |
|
iddvds |
|
114 |
21 113
|
syl |
|
115 |
114 6
|
breqtrrdi |
|
116 |
|
jm2.20nn |
|
117 |
1 33 2 116
|
syl3anc |
|
118 |
115 117
|
mpbird |
|
119 |
18
|
a1i |
|
120 |
|
dvdscmul |
|
121 |
106 110 119 120
|
syl3anc |
|
122 |
118 121
|
mpd |
|
123 |
14
|
fovcl |
|
124 |
1 22 123
|
syl2anc |
|
125 |
124
|
nn0zd |
|
126 |
|
dvdsmul1 |
|
127 |
112 125 126
|
syl2anc |
|
128 |
|
rmydbl |
|
129 |
1 22 128
|
syl2anc |
|
130 |
|
2cnd |
|
131 |
124
|
nn0cnd |
|
132 |
110
|
zcnd |
|
133 |
130 131 132
|
mul32d |
|
134 |
129 133
|
eqtrd |
|
135 |
127 134
|
breqtrrd |
|
136 |
108 112 27 122 135
|
dvdstrd |
|
137 |
4
|
oveq1d |
|
138 |
137
|
oveq2d |
|
139 |
7
|
a1i |
|
140 |
136 138 139
|
3brtr4d |
|
141 |
7 27
|
eqeltrid |
|
142 |
35
|
nngt0d |
|
143 |
|
ltrmy |
|
144 |
1 38 24 143
|
syl3anc |
|
145 |
142 144
|
mpbid |
|
146 |
29
|
eqcomd |
|
147 |
145 146 139
|
3brtr4d |
|
148 |
|
elnnz |
|
149 |
141 147 148
|
sylanbrc |
|
150 |
3
|
nnsqcld |
|
151 |
|
nnmulcl |
|
152 |
30 150 151
|
sylancr |
|
153 |
|
nndivdvds |
|
154 |
149 152 153
|
syl2anc |
|
155 |
140 154
|
mpbid |
|
156 |
|
nnm1nn0 |
|
157 |
155 156
|
syl |
|
158 |
12 157
|
eqeltrid |
|
159 |
5
|
oveq1i |
|
160 |
159
|
a1i |
|
161 |
137
|
oveq2d |
|
162 |
160 161
|
oveq12d |
|
163 |
|
rmxynorm |
|
164 |
1 13 163
|
syl2anc |
|
165 |
162 164
|
eqtrd |
|
166 |
8
|
oveq1i |
|
167 |
7
|
oveq1i |
|
168 |
167
|
oveq2i |
|
169 |
166 168
|
oveq12i |
|
170 |
|
rmxynorm |
|
171 |
1 24 170
|
syl2anc |
|
172 |
169 171
|
syl5eq |
|
173 |
165 172 85
|
3jca |
|
174 |
11
|
oveq1i |
|
175 |
10
|
oveq1i |
|
176 |
175
|
oveq2i |
|
177 |
174 176
|
oveq12i |
|
178 |
|
rmxynorm |
|
179 |
85 13 178
|
syl2anc |
|
180 |
177 179
|
syl5eq |
|
181 |
12
|
a1i |
|
182 |
181
|
oveq1d |
|
183 |
141
|
zcnd |
|
184 |
152
|
nncnd |
|
185 |
152
|
nnne0d |
|
186 |
183 184 185
|
divcld |
|
187 |
|
ax-1cn |
|
188 |
|
npcan |
|
189 |
186 187 188
|
sylancl |
|
190 |
182 189
|
eqtrd |
|
191 |
190
|
oveq1d |
|
192 |
183 184 185
|
divcan1d |
|
193 |
191 192
|
eqtr2d |
|
194 |
48
|
nn0zd |
|
195 |
81
|
nn0zd |
|
196 |
194 195
|
zmulcld |
|
197 |
|
dvdsmul1 |
|
198 |
194 196 197
|
syl2anc |
|
199 |
9
|
oveq1i |
|
200 |
57
|
nn0cnd |
|
201 |
82
|
nn0cnd |
|
202 |
200 201
|
pncan2d |
|
203 |
52
|
oveq1d |
|
204 |
81
|
nn0cnd |
|
205 |
51 51 204
|
mulassd |
|
206 |
202 203 205
|
3eqtrd |
|
207 |
199 206
|
syl5eq |
|
208 |
198 207
|
breqtrrd |
|
209 |
180 193 208
|
3jca |
|
210 |
|
zmulcl |
|
211 |
18 19 210
|
sylancr |
|
212 |
|
eluzelz |
|
213 |
1 212
|
syl |
|
214 |
82
|
nn0zd |
|
215 |
|
1z |
|
216 |
|
zsubcl |
|
217 |
215 213 216
|
sylancr |
|
218 |
|
zmulcl |
|
219 |
215 217 218
|
sylancr |
|
220 |
|
congid |
|
221 |
211 213 220
|
syl2anc |
|
222 |
54
|
nn0zd |
|
223 |
215
|
a1i |
|
224 |
3
|
nncnd |
|
225 |
130 224 224
|
mulassd |
|
226 |
224
|
sqvald |
|
227 |
226
|
oveq2d |
|
228 |
225 227
|
eqtr4d |
|
229 |
228 140
|
eqbrtrd |
|
230 |
|
muldvds1 |
|
231 |
211 19 141 230
|
syl3anc |
|
232 |
229 231
|
mpd |
|
233 |
|
zsqcl |
|
234 |
213 233
|
syl |
|
235 |
|
peano2zm |
|
236 |
234 235
|
syl |
|
237 |
236 141
|
zmulcld |
|
238 |
|
dvdsmultr2 |
|
239 |
211 237 141 238
|
syl3anc |
|
240 |
232 239
|
mpd |
|
241 |
183
|
sqvald |
|
242 |
241
|
oveq2d |
|
243 |
200
|
sqcld |
|
244 |
|
subcl |
|
245 |
243 187 244
|
sylancl |
|
246 |
245 183 183
|
mulassd |
|
247 |
242 246
|
eqtr4d |
|
248 |
240 247
|
breqtrrd |
|
249 |
51
|
sqcld |
|
250 |
183
|
sqcld |
|
251 |
245 250
|
mulcld |
|
252 |
187
|
a1i |
|
253 |
|
subsub23 |
|
254 |
249 251 252 253
|
syl3anc |
|
255 |
172 254
|
mpbid |
|
256 |
248 255
|
breqtrrd |
|
257 |
|
congsub |
|
258 |
211 222 223 213 213 256 221 257
|
syl322anc |
|
259 |
|
congmul |
|
260 |
211 222 223 195 217 256 258 259
|
syl322anc |
|
261 |
|
congadd |
|
262 |
211 213 213 214 219 221 260 261
|
syl322anc |
|
263 |
9
|
a1i |
|
264 |
217
|
zcnd |
|
265 |
264
|
mulid2d |
|
266 |
265
|
oveq2d |
|
267 |
|
pncan3 |
|
268 |
200 187 267
|
sylancl |
|
269 |
266 268
|
eqtr2d |
|
270 |
263 269
|
oveq12d |
|
271 |
262 270
|
breqtrrd |
|
272 |
|
eluzelz |
|
273 |
85 272
|
syl |
|
274 |
273 213
|
zsubcld |
|
275 |
10 89
|
eqeltrid |
|
276 |
275 19
|
zsubcld |
|
277 |
|
jm2.15nn0 |
|
278 |
85 1 92 277
|
syl3anc |
|
279 |
10
|
a1i |
|
280 |
279 4
|
oveq12d |
|
281 |
278 280
|
breqtrrd |
|
282 |
194 274 276 208 281
|
dvdstrd |
|
283 |
|
peano2zm |
|
284 |
273 283
|
syl |
|
285 |
275 13
|
zsubcld |
|
286 |
|
jm2.16nn0 |
|
287 |
85 92 286
|
syl2anc |
|
288 |
10
|
oveq1i |
|
289 |
287 288
|
breqtrrdi |
|
290 |
211 284 285 271 289
|
dvdstrd |
|
291 |
|
rmygeid |
|
292 |
1 92 291
|
syl2anc |
|
293 |
292 4
|
breqtrrd |
|
294 |
290 293
|
jca |
|
295 |
271 282 294
|
jca31 |
|
296 |
173 209 295
|
jca31 |
|
297 |
158 296
|
jca |
|
298 |
49 104 297
|
jca31 |
|