Step |
Hyp |
Ref |
Expression |
1 |
|
oveq1 |
|
2 |
1
|
breq2d |
|
3 |
|
oveq1 |
|
4 |
3
|
breq2d |
|
5 |
4
|
notbid |
|
6 |
2 5
|
anbi12d |
|
7 |
6
|
imbi1d |
|
8 |
|
oveq2 |
|
9 |
8
|
oveq2d |
|
10 |
9
|
breq2d |
|
11 |
|
oveq1 |
|
12 |
11
|
oveq2d |
|
13 |
12
|
oveq2d |
|
14 |
13
|
breq2d |
|
15 |
14
|
notbid |
|
16 |
10 15
|
anbi12d |
|
17 |
8
|
breq1d |
|
18 |
16 17
|
imbi12d |
|
19 |
18
|
ralbidv |
|
20 |
19
|
imbi2d |
|
21 |
|
oveq2 |
|
22 |
21
|
oveq2d |
|
23 |
22
|
breq2d |
|
24 |
|
oveq1 |
|
25 |
24
|
oveq2d |
|
26 |
25
|
oveq2d |
|
27 |
26
|
breq2d |
|
28 |
27
|
notbid |
|
29 |
23 28
|
anbi12d |
|
30 |
21
|
breq1d |
|
31 |
29 30
|
imbi12d |
|
32 |
31
|
ralbidv |
|
33 |
32
|
imbi2d |
|
34 |
|
oveq2 |
|
35 |
34
|
oveq2d |
|
36 |
35
|
breq2d |
|
37 |
|
oveq1 |
|
38 |
37
|
oveq2d |
|
39 |
38
|
oveq2d |
|
40 |
39
|
breq2d |
|
41 |
40
|
notbid |
|
42 |
36 41
|
anbi12d |
|
43 |
34
|
breq1d |
|
44 |
42 43
|
imbi12d |
|
45 |
44
|
ralbidv |
|
46 |
45
|
imbi2d |
|
47 |
|
oveq2 |
|
48 |
47
|
oveq2d |
|
49 |
48
|
breq2d |
|
50 |
|
oveq1 |
|
51 |
50
|
oveq2d |
|
52 |
51
|
oveq2d |
|
53 |
52
|
breq2d |
|
54 |
53
|
notbid |
|
55 |
49 54
|
anbi12d |
|
56 |
47
|
breq1d |
|
57 |
55 56
|
imbi12d |
|
58 |
57
|
ralbidv |
|
59 |
58
|
imbi2d |
|
60 |
|
breq1 |
|
61 |
|
breq1 |
|
62 |
61
|
notbid |
|
63 |
60 62
|
anbi12d |
|
64 |
|
breq2 |
|
65 |
63 64
|
imbi12d |
|
66 |
65
|
imbi2d |
|
67 |
|
simplrl |
|
68 |
|
simpll |
|
69 |
|
coprm |
|
70 |
67 68 69
|
syl2anc |
|
71 |
|
zcn |
|
72 |
71
|
ad2antll |
|
73 |
|
prmz |
|
74 |
73
|
ad2antrl |
|
75 |
74
|
zcnd |
|
76 |
72 75
|
mulcomd |
|
77 |
76
|
breq2d |
|
78 |
|
simpl |
|
79 |
74 78
|
gcdcomd |
|
80 |
79
|
eqeq1d |
|
81 |
77 80
|
anbi12d |
|
82 |
|
simprr |
|
83 |
|
coprmdvds |
|
84 |
78 74 82 83
|
syl3anc |
|
85 |
81 84
|
sylbid |
|
86 |
85
|
expdimp |
|
87 |
70 86
|
sylbid |
|
88 |
87
|
con1d |
|
89 |
88
|
expimpd |
|
90 |
89
|
ex |
|
91 |
66 90
|
vtoclga |
|
92 |
91
|
impl |
|
93 |
73
|
zcnd |
|
94 |
93
|
exp1d |
|
95 |
94
|
ad2antlr |
|
96 |
95
|
oveq2d |
|
97 |
96
|
breq2d |
|
98 |
|
1m1e0 |
|
99 |
98
|
oveq2i |
|
100 |
73
|
ad2antlr |
|
101 |
100
|
zcnd |
|
102 |
101
|
exp0d |
|
103 |
99 102
|
syl5eq |
|
104 |
103
|
oveq2d |
|
105 |
71
|
adantl |
|
106 |
105
|
mulid1d |
|
107 |
104 106
|
eqtrd |
|
108 |
107
|
breq2d |
|
109 |
108
|
notbid |
|
110 |
97 109
|
anbi12d |
|
111 |
101
|
exp1d |
|
112 |
111
|
breq1d |
|
113 |
92 110 112
|
3imtr4d |
|
114 |
113
|
ralrimiva |
|
115 |
|
oveq1 |
|
116 |
115
|
breq2d |
|
117 |
|
oveq1 |
|
118 |
117
|
breq2d |
|
119 |
118
|
notbid |
|
120 |
116 119
|
anbi12d |
|
121 |
120
|
imbi1d |
|
122 |
121
|
cbvralvw |
|
123 |
|
simprr |
|
124 |
73
|
ad2antrl |
|
125 |
123 124
|
zmulcld |
|
126 |
|
oveq1 |
|
127 |
126
|
breq2d |
|
128 |
|
oveq1 |
|
129 |
128
|
breq2d |
|
130 |
129
|
notbid |
|
131 |
127 130
|
anbi12d |
|
132 |
131
|
imbi1d |
|
133 |
132
|
rspcv |
|
134 |
125 133
|
syl |
|
135 |
|
nnnn0 |
|
136 |
135
|
ad2antrr |
|
137 |
|
zexpcl |
|
138 |
124 136 137
|
syl2anc |
|
139 |
|
simplr |
|
140 |
|
divides |
|
141 |
138 139 140
|
syl2anc |
|
142 |
89
|
adantll |
|
143 |
|
prmnn |
|
144 |
143
|
ad2antrl |
|
145 |
144
|
nncnd |
|
146 |
135
|
ad2antrr |
|
147 |
145 146
|
expp1d |
|
148 |
144 146
|
nnexpcld |
|
149 |
148
|
nncnd |
|
150 |
149 145
|
mulcomd |
|
151 |
147 150
|
eqtrd |
|
152 |
151
|
oveq2d |
|
153 |
71
|
ad2antll |
|
154 |
153 145 149
|
mulassd |
|
155 |
152 154
|
eqtr4d |
|
156 |
155
|
breq2d |
|
157 |
|
simplr |
|
158 |
|
simprr |
|
159 |
144
|
nnzd |
|
160 |
158 159
|
zmulcld |
|
161 |
148
|
nnzd |
|
162 |
148
|
nnne0d |
|
163 |
|
dvdsmulcr |
|
164 |
157 160 161 162 163
|
syl112anc |
|
165 |
156 164
|
bitrd |
|
166 |
|
dvdsmulcr |
|
167 |
157 158 161 162 166
|
syl112anc |
|
168 |
167
|
notbid |
|
169 |
165 168
|
anbi12d |
|
170 |
151
|
breq1d |
|
171 |
|
dvdsmulcr |
|
172 |
159 157 161 162 171
|
syl112anc |
|
173 |
170 172
|
bitrd |
|
174 |
142 169 173
|
3imtr4d |
|
175 |
174
|
an32s |
|
176 |
|
breq1 |
|
177 |
|
breq1 |
|
178 |
177
|
notbid |
|
179 |
176 178
|
anbi12d |
|
180 |
|
breq2 |
|
181 |
179 180
|
imbi12d |
|
182 |
175 181
|
syl5ibcom |
|
183 |
182
|
rexlimdva |
|
184 |
183
|
adantlr |
|
185 |
141 184
|
sylbid |
|
186 |
185
|
com23 |
|
187 |
186
|
a2d |
|
188 |
71
|
ad2antll |
|
189 |
124
|
zcnd |
|
190 |
138
|
zcnd |
|
191 |
188 189 190
|
mulassd |
|
192 |
189 190
|
mulcomd |
|
193 |
189 136
|
expp1d |
|
194 |
192 193
|
eqtr4d |
|
195 |
194
|
oveq2d |
|
196 |
191 195
|
eqtrd |
|
197 |
196
|
breq2d |
|
198 |
|
nnm1nn0 |
|
199 |
198
|
ad2antrr |
|
200 |
|
zexpcl |
|
201 |
124 199 200
|
syl2anc |
|
202 |
201
|
zcnd |
|
203 |
188 189 202
|
mulassd |
|
204 |
189 202
|
mulcomd |
|
205 |
|
simpll |
|
206 |
|
expm1t |
|
207 |
189 205 206
|
syl2anc |
|
208 |
204 207
|
eqtr4d |
|
209 |
208
|
oveq2d |
|
210 |
203 209
|
eqtrd |
|
211 |
210
|
breq2d |
|
212 |
211
|
notbid |
|
213 |
197 212
|
anbi12d |
|
214 |
213
|
imbi1d |
|
215 |
|
nncn |
|
216 |
215
|
ad2antrr |
|
217 |
|
ax-1cn |
|
218 |
|
pncan |
|
219 |
216 217 218
|
sylancl |
|
220 |
219
|
oveq2d |
|
221 |
220
|
oveq2d |
|
222 |
221
|
breq2d |
|
223 |
222
|
notbid |
|
224 |
223
|
anbi2d |
|
225 |
224
|
imbi1d |
|
226 |
187 214 225
|
3imtr4d |
|
227 |
134 226
|
syld |
|
228 |
227
|
anassrs |
|
229 |
228
|
ralrimdva |
|
230 |
122 229
|
syl5bi |
|
231 |
230
|
expl |
|
232 |
231
|
a2d |
|
233 |
20 33 46 59 114 232
|
nnind |
|
234 |
233
|
com12 |
|
235 |
234
|
impr |
|
236 |
235
|
adantll |
|
237 |
|
simpll |
|
238 |
7 236 237
|
rspcdva |
|
239 |
238
|
3impia |
|