Step |
Hyp |
Ref |
Expression |
1 |
|
nn0ex |
|
2 |
|
simpr |
|
3 |
|
elmapg |
|
4 |
1 2 3
|
sylancr |
|
5 |
|
oveq1 |
|
6 |
5
|
eleq1d |
|
7 |
6
|
ralbidv |
|
8 |
7
|
imbi2d |
|
9 |
|
oveq1 |
|
10 |
9
|
eleq1d |
|
11 |
10
|
ralbidv |
|
12 |
11
|
imbi2d |
|
13 |
|
oveq1 |
|
14 |
13
|
eleq1d |
|
15 |
14
|
ralbidv |
|
16 |
15
|
imbi2d |
|
17 |
|
oveq1 |
|
18 |
17
|
eleq1d |
|
19 |
18
|
ralbidv |
|
20 |
19
|
imbi2d |
|
21 |
|
elmapi |
|
22 |
|
0ramcl |
|
23 |
21 22
|
sylan2 |
|
24 |
23
|
ralrimiva |
|
25 |
|
oveq2 |
|
26 |
25
|
eleq1d |
|
27 |
26
|
cbvralvw |
|
28 |
|
simpll |
|
29 |
21
|
ad2antrl |
|
30 |
29
|
ffvelrnda |
|
31 |
28 30
|
fsumnn0cl |
|
32 |
|
eqeq2 |
|
33 |
32
|
anbi2d |
|
34 |
33
|
imbi1d |
|
35 |
34
|
albidv |
|
36 |
35
|
imbi2d |
|
37 |
|
eqeq2 |
|
38 |
37
|
anbi2d |
|
39 |
38
|
imbi1d |
|
40 |
39
|
albidv |
|
41 |
40
|
imbi2d |
|
42 |
|
eqeq2 |
|
43 |
42
|
anbi2d |
|
44 |
43
|
imbi1d |
|
45 |
44
|
albidv |
|
46 |
45
|
imbi2d |
|
47 |
|
eqeq2 |
|
48 |
47
|
anbi2d |
|
49 |
48
|
imbi1d |
|
50 |
49
|
albidv |
|
51 |
50
|
imbi2d |
|
52 |
|
simplll |
|
53 |
|
ffvelrn |
|
54 |
53
|
adantll |
|
55 |
54
|
nn0red |
|
56 |
54
|
nn0ge0d |
|
57 |
52 55 56
|
fsum00 |
|
58 |
|
fvex |
|
59 |
58
|
rgenw |
|
60 |
|
mpteqb |
|
61 |
59 60
|
ax-mp |
|
62 |
57 61
|
bitr4di |
|
63 |
|
simpr |
|
64 |
63
|
feqmptd |
|
65 |
|
fconstmpt |
|
66 |
65
|
a1i |
|
67 |
64 66
|
eqeq12d |
|
68 |
62 67
|
bitr4d |
|
69 |
|
xpeq1 |
|
70 |
|
0xp |
|
71 |
69 70
|
eqtrdi |
|
72 |
71
|
oveq2d |
|
73 |
|
simpllr |
|
74 |
|
peano2nn0 |
|
75 |
73 74
|
syl |
|
76 |
|
ram0 |
|
77 |
75 76
|
syl |
|
78 |
72 77
|
sylan9eqr |
|
79 |
75
|
adantr |
|
80 |
78 79
|
eqeltrd |
|
81 |
75
|
adantr |
|
82 |
|
simp-4l |
|
83 |
|
simpr |
|
84 |
|
ramz |
|
85 |
81 82 83 84
|
syl3anc |
|
86 |
|
0nn0 |
|
87 |
85 86
|
eqeltrdi |
|
88 |
80 87
|
pm2.61dane |
|
89 |
|
oveq2 |
|
90 |
89
|
eleq1d |
|
91 |
88 90
|
syl5ibrcom |
|
92 |
68 91
|
sylbid |
|
93 |
92
|
expimpd |
|
94 |
93
|
alrimiv |
|
95 |
|
ffn |
|
96 |
95
|
ad2antrl |
|
97 |
|
ffnfv |
|
98 |
97
|
baib |
|
99 |
96 98
|
syl |
|
100 |
|
simplr |
|
101 |
100
|
ad2antrr |
|
102 |
101 74
|
syl |
|
103 |
|
simp-4l |
|
104 |
|
simprr |
|
105 |
|
nnssnn0 |
|
106 |
|
fss |
|
107 |
104 105 106
|
sylancl |
|
108 |
101
|
nn0cnd |
|
109 |
|
ax-1cn |
|
110 |
|
pncan |
|
111 |
108 109 110
|
sylancl |
|
112 |
111
|
oveq1d |
|
113 |
|
oveq2 |
|
114 |
113
|
eleq1d |
|
115 |
|
simprl |
|
116 |
115
|
ad2antrr |
|
117 |
103
|
adantr |
|
118 |
117
|
mptexd |
|
119 |
|
simpllr |
|
120 |
104
|
ffvelrnda |
|
121 |
|
nnm1nn0 |
|
122 |
120 121
|
syl |
|
123 |
122
|
adantr |
|
124 |
107
|
adantr |
|
125 |
124
|
ffvelrnda |
|
126 |
123 125
|
ifcld |
|
127 |
126
|
fmpttd |
|
128 |
|
simplrr |
|
129 |
|
simpr |
|
130 |
|
ffvelrn |
|
131 |
130
|
3ad2antl2 |
|
132 |
131
|
nncnd |
|
133 |
132
|
subid1d |
|
134 |
133
|
ifeq2d |
|
135 |
|
fveq2 |
|
136 |
135
|
adantl |
|
137 |
136
|
oveq1d |
|
138 |
137
|
ifeq1da |
|
139 |
134 138
|
eqtr2d |
|
140 |
|
ovif2 |
|
141 |
139 140
|
eqtr4di |
|
142 |
141
|
sumeq2dv |
|
143 |
|
simp1 |
|
144 |
|
0cn |
|
145 |
109 144
|
ifcli |
|
146 |
145
|
a1i |
|
147 |
143 132 146
|
fsumsub |
|
148 |
|
elsng |
|
149 |
148
|
ifbid |
|
150 |
149
|
sumeq2i |
|
151 |
|
simp3 |
|
152 |
151
|
snssd |
|
153 |
|
sumhash |
|
154 |
143 152 153
|
syl2anc |
|
155 |
|
hashsng |
|
156 |
151 155
|
syl |
|
157 |
154 156
|
eqtrd |
|
158 |
150 157
|
syl5eqr |
|
159 |
158
|
oveq2d |
|
160 |
142 147 159
|
3eqtrd |
|
161 |
117 128 129 160
|
syl3anc |
|
162 |
|
simplrl |
|
163 |
162
|
oveq1d |
|
164 |
|
simplrr |
|
165 |
164
|
ad2antrr |
|
166 |
165
|
nn0cnd |
|
167 |
|
pncan |
|
168 |
166 109 167
|
sylancl |
|
169 |
161 163 168
|
3eqtrd |
|
170 |
127 169
|
jca |
|
171 |
|
feq1 |
|
172 |
|
fveq1 |
|
173 |
|
equequ1 |
|
174 |
|
fveq2 |
|
175 |
173 174
|
ifbieq2d |
|
176 |
|
eqid |
|
177 |
|
ovex |
|
178 |
|
fvex |
|
179 |
177 178
|
ifex |
|
180 |
175 176 179
|
fvmpt |
|
181 |
172 180
|
sylan9eq |
|
182 |
181
|
sumeq2dv |
|
183 |
182
|
eqeq1d |
|
184 |
171 183
|
anbi12d |
|
185 |
|
oveq2 |
|
186 |
185
|
eleq1d |
|
187 |
184 186
|
imbi12d |
|
188 |
187
|
spcgv |
|
189 |
118 119 170 188
|
syl3c |
|
190 |
189
|
fmpttd |
|
191 |
|
elmapg |
|
192 |
1 103 191
|
sylancr |
|
193 |
190 192
|
mpbird |
|
194 |
114 116 193
|
rspcdva |
|
195 |
112 194
|
eqeltrd |
|
196 |
|
peano2nn0 |
|
197 |
195 196
|
syl |
|
198 |
|
nn0p1nn |
|
199 |
100 198
|
syl |
|
200 |
199
|
ad2antrr |
|
201 |
|
equequ1 |
|
202 |
|
fveq2 |
|
203 |
201 202
|
ifbieq2d |
|
204 |
203
|
cbvmptv |
|
205 |
|
eqeq2 |
|
206 |
|
fveq2 |
|
207 |
206
|
oveq1d |
|
208 |
205 207
|
ifbieq1d |
|
209 |
208
|
mpteq2dv |
|
210 |
204 209
|
syl5eq |
|
211 |
210
|
oveq2d |
|
212 |
211
|
cbvmptv |
|
213 |
200 103 104 212 190 195
|
ramub1 |
|
214 |
|
ramubcl |
|
215 |
102 103 107 197 213 214
|
syl32anc |
|
216 |
215
|
expr |
|
217 |
216
|
adantrl |
|
218 |
99 217
|
sylbird |
|
219 |
|
rexnal |
|
220 |
|
simprl |
|
221 |
220
|
ffvelrnda |
|
222 |
|
elnn0 |
|
223 |
221 222
|
sylib |
|
224 |
223
|
ord |
|
225 |
199
|
ad2antrr |
|
226 |
|
simp-4l |
|
227 |
225 226 220
|
3jca |
|
228 |
|
ramz2 |
|
229 |
227 228
|
sylan |
|
230 |
229 86
|
eqeltrdi |
|
231 |
230
|
expr |
|
232 |
224 231
|
syld |
|
233 |
232
|
rexlimdva |
|
234 |
219 233
|
syl5bir |
|
235 |
218 234
|
pm2.61d |
|
236 |
235
|
exp31 |
|
237 |
236
|
alrimdv |
|
238 |
|
feq1 |
|
239 |
|
fveq1 |
|
240 |
239
|
sumeq2sdv |
|
241 |
240
|
eqeq1d |
|
242 |
238 241
|
anbi12d |
|
243 |
|
oveq2 |
|
244 |
243
|
eleq1d |
|
245 |
242 244
|
imbi12d |
|
246 |
245
|
cbvalvw |
|
247 |
237 246
|
syl6ibr |
|
248 |
247
|
anassrs |
|
249 |
248
|
expcom |
|
250 |
249
|
a2d |
|
251 |
36 41 46 51 94 250
|
nn0ind |
|
252 |
251
|
com12 |
|
253 |
252
|
adantrl |
|
254 |
31 253
|
mpd |
|
255 |
240
|
biantrud |
|
256 |
255 238
|
bitr3d |
|
257 |
256 244
|
imbi12d |
|
258 |
257
|
spvv |
|
259 |
254 29 258
|
sylc |
|
260 |
259
|
expr |
|
261 |
260
|
ralrimdva |
|
262 |
27 261
|
syl5bi |
|
263 |
262
|
expcom |
|
264 |
263
|
a2d |
|
265 |
8 12 16 20 24 264
|
nn0ind |
|
266 |
265
|
imp |
|
267 |
|
oveq2 |
|
268 |
267
|
eleq1d |
|
269 |
268
|
rspccv |
|
270 |
266 269
|
syl |
|
271 |
4 270
|
sylbird |
|
272 |
271
|
3impia |
|