Step |
Hyp |
Ref |
Expression |
1 |
|
oddpwdc.j |
|
2 |
|
oddpwdc.f |
|
3 |
|
2nn |
|
4 |
3
|
a1i |
|
5 |
|
simpl |
|
6 |
4 5
|
nnexpcld |
|
7 |
|
ssrab2 |
|
8 |
1 7
|
eqsstri |
|
9 |
|
simpr |
|
10 |
8 9
|
sseldi |
|
11 |
6 10
|
nnmulcld |
|
12 |
11
|
ancoms |
|
13 |
12
|
adantl |
|
14 |
|
id |
|
15 |
3
|
a1i |
|
16 |
|
nn0ssre |
|
17 |
|
ltso |
|
18 |
|
soss |
|
19 |
16 17 18
|
mp2 |
|
20 |
19
|
a1i |
|
21 |
|
0zd |
|
22 |
|
ssrab2 |
|
23 |
22
|
a1i |
|
24 |
|
nnz |
|
25 |
|
oveq2 |
|
26 |
25
|
breq1d |
|
27 |
26
|
elrab |
|
28 |
|
simprl |
|
29 |
28
|
nn0red |
|
30 |
3
|
a1i |
|
31 |
30 28
|
nnexpcld |
|
32 |
31
|
nnred |
|
33 |
|
simpl |
|
34 |
33
|
nnred |
|
35 |
|
2re |
|
36 |
35
|
leidi |
|
37 |
|
nexple |
|
38 |
35 36 37
|
mp3an23 |
|
39 |
38
|
ad2antrl |
|
40 |
31
|
nnzd |
|
41 |
|
simprr |
|
42 |
|
dvdsle |
|
43 |
42
|
imp |
|
44 |
40 33 41 43
|
syl21anc |
|
45 |
29 32 34 39 44
|
letrd |
|
46 |
27 45
|
sylan2b |
|
47 |
46
|
ralrimiva |
|
48 |
|
brralrspcev |
|
49 |
24 47 48
|
syl2anc |
|
50 |
|
nn0uz |
|
51 |
50
|
uzsupss |
|
52 |
21 23 49 51
|
syl3anc |
|
53 |
20 52
|
supcl |
|
54 |
15 53
|
nnexpcld |
|
55 |
|
fzfi |
|
56 |
|
0zd |
|
57 |
24
|
adantr |
|
58 |
27 28
|
sylan2b |
|
59 |
58
|
nn0zd |
|
60 |
58
|
nn0ge0d |
|
61 |
|
elfz4 |
|
62 |
56 57 59 60 46 61
|
syl32anc |
|
63 |
62
|
ex |
|
64 |
63
|
ssrdv |
|
65 |
|
ssfi |
|
66 |
55 64 65
|
sylancr |
|
67 |
|
0nn0 |
|
68 |
67
|
a1i |
|
69 |
|
2cn |
|
70 |
|
exp0 |
|
71 |
69 70
|
ax-mp |
|
72 |
|
1dvds |
|
73 |
24 72
|
syl |
|
74 |
71 73
|
eqbrtrid |
|
75 |
|
oveq2 |
|
76 |
75
|
breq1d |
|
77 |
76
|
elrab |
|
78 |
68 74 77
|
sylanbrc |
|
79 |
78
|
ne0d |
|
80 |
|
fisupcl |
|
81 |
20 66 79 23 80
|
syl13anc |
|
82 |
|
oveq2 |
|
83 |
82
|
breq1d |
|
84 |
83
|
cbvrabv |
|
85 |
81 84
|
eleqtrdi |
|
86 |
|
oveq2 |
|
87 |
86
|
breq1d |
|
88 |
87
|
elrab |
|
89 |
85 88
|
sylib |
|
90 |
89
|
simprd |
|
91 |
|
nndivdvds |
|
92 |
91
|
biimpa |
|
93 |
14 54 90 92
|
syl21anc |
|
94 |
|
1nn0 |
|
95 |
94
|
a1i |
|
96 |
53 95
|
nn0addcld |
|
97 |
53
|
nn0red |
|
98 |
97
|
ltp1d |
|
99 |
20 52
|
supub |
|
100 |
98 99
|
mt2d |
|
101 |
84
|
eleq2i |
|
102 |
100 101
|
sylnib |
|
103 |
|
oveq2 |
|
104 |
103
|
breq1d |
|
105 |
104
|
elrab |
|
106 |
102 105
|
sylnib |
|
107 |
|
imnan |
|
108 |
106 107
|
sylibr |
|
109 |
96 108
|
mpd |
|
110 |
|
expp1 |
|
111 |
69 53 110
|
sylancr |
|
112 |
111
|
breq1d |
|
113 |
109 112
|
mtbid |
|
114 |
|
nncn |
|
115 |
54
|
nncnd |
|
116 |
54
|
nnne0d |
|
117 |
114 115 116
|
divcan2d |
|
118 |
117
|
eqcomd |
|
119 |
118
|
breq2d |
|
120 |
15
|
nnzd |
|
121 |
93
|
nnzd |
|
122 |
54
|
nnzd |
|
123 |
|
dvdscmulr |
|
124 |
120 121 122 116 123
|
syl112anc |
|
125 |
119 124
|
bitrd |
|
126 |
113 125
|
mtbid |
|
127 |
|
breq2 |
|
128 |
127
|
notbid |
|
129 |
128 1
|
elrab2 |
|
130 |
93 126 129
|
sylanbrc |
|
131 |
130 53
|
jca |
|
132 |
131
|
adantl |
|
133 |
|
simpr |
|
134 |
3
|
a1i |
|
135 |
|
simplr |
|
136 |
134 135
|
nnexpcld |
|
137 |
8
|
sseli |
|
138 |
137
|
ad2antrr |
|
139 |
136 138
|
nnmulcld |
|
140 |
133 139
|
eqeltrd |
|
141 |
|
simplll |
|
142 |
|
breq2 |
|
143 |
142
|
notbid |
|
144 |
143 1
|
elrab2 |
|
145 |
144
|
simprbi |
|
146 |
|
2z |
|
147 |
135
|
adantr |
|
148 |
147
|
nn0zd |
|
149 |
19
|
a1i |
|
150 |
140 52
|
syl |
|
151 |
150
|
adantr |
|
152 |
149 151
|
supcl |
|
153 |
152
|
nn0zd |
|
154 |
|
simpr |
|
155 |
|
znnsub |
|
156 |
155
|
biimpa |
|
157 |
148 153 154 156
|
syl21anc |
|
158 |
|
iddvdsexp |
|
159 |
146 157 158
|
sylancr |
|
160 |
146
|
a1i |
|
161 |
140 121
|
syl |
|
162 |
161
|
adantr |
|
163 |
157
|
nnnn0d |
|
164 |
|
zexpcl |
|
165 |
146 163 164
|
sylancr |
|
166 |
|
dvdsmultr2 |
|
167 |
160 162 165 166
|
syl3anc |
|
168 |
159 167
|
mpd |
|
169 |
138
|
adantr |
|
170 |
169
|
nncnd |
|
171 |
|
2cnd |
|
172 |
171 163
|
expcld |
|
173 |
140
|
adantr |
|
174 |
173
|
nncnd |
|
175 |
173 115
|
syl |
|
176 |
|
2ne0 |
|
177 |
176
|
a1i |
|
178 |
171 177 153
|
expne0d |
|
179 |
174 175 178
|
divcld |
|
180 |
172 179
|
mulcld |
|
181 |
171 147
|
expcld |
|
182 |
171 177 148
|
expne0d |
|
183 |
173 118
|
syl |
|
184 |
|
simplr |
|
185 |
147
|
nn0cnd |
|
186 |
152
|
nn0cnd |
|
187 |
185 186
|
pncan3d |
|
188 |
187
|
oveq2d |
|
189 |
171 163 147
|
expaddd |
|
190 |
188 189
|
eqtr3d |
|
191 |
190
|
oveq1d |
|
192 |
183 184 191
|
3eqtr3d |
|
193 |
181 172 179
|
mulassd |
|
194 |
192 193
|
eqtrd |
|
195 |
170 180 181 182 194
|
mulcanad |
|
196 |
179 172
|
mulcomd |
|
197 |
195 196
|
eqtr4d |
|
198 |
168 197
|
breqtrrd |
|
199 |
145 198
|
nsyl3 |
|
200 |
141 199
|
pm2.65da |
|
201 |
138
|
nnzd |
|
202 |
136
|
nnzd |
|
203 |
140
|
nnzd |
|
204 |
136
|
nncnd |
|
205 |
138
|
nncnd |
|
206 |
204 205
|
mulcomd |
|
207 |
133 206
|
eqtr2d |
|
208 |
|
dvds0lem |
|
209 |
201 202 203 207 208
|
syl31anc |
|
210 |
|
oveq2 |
|
211 |
210
|
breq1d |
|
212 |
211
|
elrab |
|
213 |
135 209 212
|
sylanbrc |
|
214 |
19
|
a1i |
|
215 |
214 150
|
supub |
|
216 |
213 215
|
mpd |
|
217 |
135
|
nn0red |
|
218 |
140 97
|
syl |
|
219 |
217 218
|
lttri3d |
|
220 |
200 216 219
|
mpbir2and |
|
221 |
|
simplr |
|
222 |
140
|
adantr |
|
223 |
222
|
nncnd |
|
224 |
138
|
adantr |
|
225 |
224
|
nncnd |
|
226 |
|
nnexpcl |
|
227 |
3 226
|
mpan |
|
228 |
227
|
nncnd |
|
229 |
227
|
nnne0d |
|
230 |
228 229
|
jca |
|
231 |
230
|
ad3antlr |
|
232 |
|
divmul2 |
|
233 |
223 225 231 232
|
syl3anc |
|
234 |
221 233
|
mpbird |
|
235 |
|
simpr |
|
236 |
235
|
oveq2d |
|
237 |
236
|
oveq2d |
|
238 |
234 237
|
eqtr3d |
|
239 |
238
|
ex |
|
240 |
220 239
|
jcai |
|
241 |
240
|
ancomd |
|
242 |
140 241
|
jca |
|
243 |
|
simprl |
|
244 |
130
|
adantr |
|
245 |
243 244
|
eqeltrd |
|
246 |
|
simprr |
|
247 |
53
|
adantr |
|
248 |
246 247
|
eqeltrd |
|
249 |
118
|
adantr |
|
250 |
246
|
oveq2d |
|
251 |
250 243
|
oveq12d |
|
252 |
249 251
|
eqtr4d |
|
253 |
245 248 252
|
jca31 |
|
254 |
242 253
|
impbii |
|
255 |
254
|
a1i |
|
256 |
2 13 132 255
|
f1od2 |
|
257 |
256
|
mptru |
|