Step |
Hyp |
Ref |
Expression |
1 |
|
fourierdlem54.t |
|
2 |
|
fourierdlem54.p |
|
3 |
|
fourierdlem54.m |
|
4 |
|
fourierdlem54.q |
|
5 |
|
fourierdlem54.c |
|
6 |
|
fourierdlem54.d |
|
7 |
|
fourierdlem54.cd |
|
8 |
|
fourierdlem54.o |
|
9 |
|
fourierdlem54.h |
|
10 |
|
fourierdlem54.n |
|
11 |
|
fourierdlem54.s |
|
12 |
|
2z |
|
13 |
12
|
a1i |
|
14 |
|
prid1g |
|
15 |
|
elun1 |
|
16 |
5 14 15
|
3syl |
|
17 |
16 9
|
eleqtrrdi |
|
18 |
17
|
ne0d |
|
19 |
|
prfi |
|
20 |
2 3 4
|
fourierdlem11 |
|
21 |
20
|
simp1d |
|
22 |
20
|
simp2d |
|
23 |
20
|
simp3d |
|
24 |
2 3 4
|
fourierdlem15 |
|
25 |
|
frn |
|
26 |
24 25
|
syl |
|
27 |
2
|
fourierdlem2 |
|
28 |
3 27
|
syl |
|
29 |
4 28
|
mpbid |
|
30 |
29
|
simpld |
|
31 |
|
elmapi |
|
32 |
|
ffn |
|
33 |
30 31 32
|
3syl |
|
34 |
|
fzfid |
|
35 |
|
fnfi |
|
36 |
33 34 35
|
syl2anc |
|
37 |
|
rnfi |
|
38 |
36 37
|
syl |
|
39 |
29
|
simprd |
|
40 |
39
|
simpld |
|
41 |
40
|
simpld |
|
42 |
3
|
nnnn0d |
|
43 |
|
nn0uz |
|
44 |
42 43
|
eleqtrdi |
|
45 |
|
eluzfz1 |
|
46 |
44 45
|
syl |
|
47 |
|
fnfvelrn |
|
48 |
33 46 47
|
syl2anc |
|
49 |
41 48
|
eqeltrrd |
|
50 |
40
|
simprd |
|
51 |
|
eluzfz2 |
|
52 |
44 51
|
syl |
|
53 |
|
fnfvelrn |
|
54 |
33 52 53
|
syl2anc |
|
55 |
50 54
|
eqeltrrd |
|
56 |
|
eqid |
|
57 |
|
eqid |
|
58 |
|
eqid |
|
59 |
|
eqid |
|
60 |
|
eqid |
|
61 |
|
eqid |
|
62 |
|
oveq1 |
|
63 |
62
|
eleq1d |
|
64 |
63
|
rexbidv |
|
65 |
64
|
cbvrabv |
|
66 |
|
oveq1 |
|
67 |
66
|
oveq2d |
|
68 |
67
|
eleq1d |
|
69 |
68
|
anbi1d |
|
70 |
|
oveq1 |
|
71 |
70
|
oveq2d |
|
72 |
71
|
eleq1d |
|
73 |
72
|
anbi2d |
|
74 |
69 73
|
cbvrex2vw |
|
75 |
74
|
anbi2i |
|
76 |
21 22 23 1 26 38 49 55 56 57 58 59 5 6 60 61 65 75
|
fourierdlem42 |
|
77 |
|
unfi |
|
78 |
19 76 77
|
sylancr |
|
79 |
9 78
|
eqeltrid |
|
80 |
|
hashnncl |
|
81 |
79 80
|
syl |
|
82 |
18 81
|
mpbird |
|
83 |
82
|
nnzd |
|
84 |
5 7
|
ltned |
|
85 |
|
hashprg |
|
86 |
5 6 85
|
syl2anc |
|
87 |
84 86
|
mpbid |
|
88 |
87
|
eqcomd |
|
89 |
|
ssun1 |
|
90 |
89
|
a1i |
|
91 |
90 9
|
sseqtrrdi |
|
92 |
|
hashssle |
|
93 |
79 91 92
|
syl2anc |
|
94 |
88 93
|
eqbrtrd |
|
95 |
|
eluz2 |
|
96 |
13 83 94 95
|
syl3anbrc |
|
97 |
|
uz2m1nn |
|
98 |
96 97
|
syl |
|
99 |
10 98
|
eqeltrid |
|
100 |
|
prssg |
|
101 |
5 6 100
|
syl2anc |
|
102 |
5 6 101
|
mpbi2and |
|
103 |
|
ssrab2 |
|
104 |
5 6
|
iccssred |
|
105 |
103 104
|
sstrid |
|
106 |
102 105
|
unssd |
|
107 |
9 106
|
eqsstrid |
|
108 |
79 107 11 10
|
fourierdlem36 |
|
109 |
|
df-isom |
|
110 |
108 109
|
sylib |
|
111 |
110
|
simpld |
|
112 |
|
f1of |
|
113 |
111 112
|
syl |
|
114 |
113 107
|
fssd |
|
115 |
|
reex |
|
116 |
|
ovex |
|
117 |
116
|
a1i |
|
118 |
|
elmapg |
|
119 |
115 117 118
|
sylancr |
|
120 |
114 119
|
mpbird |
|
121 |
|
df-f1o |
|
122 |
111 121
|
sylib |
|
123 |
122
|
simprd |
|
124 |
|
dffo3 |
|
125 |
123 124
|
sylib |
|
126 |
125
|
simprd |
|
127 |
|
eqeq1 |
|
128 |
|
eqcom |
|
129 |
127 128
|
syl6bb |
|
130 |
129
|
rexbidv |
|
131 |
130
|
rspcv |
|
132 |
17 126 131
|
sylc |
|
133 |
|
fveq2 |
|
134 |
133
|
eqcomd |
|
135 |
134
|
adantl |
|
136 |
|
simplr |
|
137 |
135 136
|
eqtrd |
|
138 |
5
|
ad2antrr |
|
139 |
137 138
|
eqeltrd |
|
140 |
139 137
|
eqled |
|
141 |
140
|
3adantl2 |
|
142 |
5
|
rexrd |
|
143 |
6
|
rexrd |
|
144 |
5 6 7
|
ltled |
|
145 |
|
lbicc2 |
|
146 |
142 143 144 145
|
syl3anc |
|
147 |
|
ubicc2 |
|
148 |
142 143 144 147
|
syl3anc |
|
149 |
|
prssg |
|
150 |
146 148 149
|
syl2anc |
|
151 |
146 148 150
|
mpbi2and |
|
152 |
103
|
a1i |
|
153 |
151 152
|
unssd |
|
154 |
9 153
|
eqsstrid |
|
155 |
|
nnm1nn0 |
|
156 |
82 155
|
syl |
|
157 |
10 156
|
eqeltrid |
|
158 |
157 43
|
eleqtrdi |
|
159 |
|
eluzfz1 |
|
160 |
158 159
|
syl |
|
161 |
113 160
|
ffvelrnd |
|
162 |
154 161
|
sseldd |
|
163 |
104 162
|
sseldd |
|
164 |
163
|
adantr |
|
165 |
164
|
3ad2antl1 |
|
166 |
5
|
adantr |
|
167 |
166
|
3ad2antl1 |
|
168 |
|
elfzelz |
|
169 |
168
|
zred |
|
170 |
169
|
adantr |
|
171 |
|
elfzle1 |
|
172 |
171
|
adantr |
|
173 |
|
neqne |
|
174 |
173
|
adantl |
|
175 |
170 172 174
|
ne0gt0d |
|
176 |
175
|
3ad2antl2 |
|
177 |
|
simpl1 |
|
178 |
|
simpl2 |
|
179 |
110
|
simprd |
|
180 |
|
breq1 |
|
181 |
|
fveq2 |
|
182 |
181
|
breq1d |
|
183 |
180 182
|
bibi12d |
|
184 |
183
|
ralbidv |
|
185 |
184
|
rspcv |
|
186 |
160 179 185
|
sylc |
|
187 |
186
|
r19.21bi |
|
188 |
177 178 187
|
syl2anc |
|
189 |
176 188
|
mpbid |
|
190 |
|
simpl3 |
|
191 |
189 190
|
breqtrd |
|
192 |
165 167 191
|
ltled |
|
193 |
141 192
|
pm2.61dan |
|
194 |
193
|
rexlimdv3a |
|
195 |
132 194
|
mpd |
|
196 |
|
elicc2 |
|
197 |
5 6 196
|
syl2anc |
|
198 |
162 197
|
mpbid |
|
199 |
198
|
simp2d |
|
200 |
163 5
|
letri3d |
|
201 |
195 199 200
|
mpbir2and |
|
202 |
|
eluzfz2 |
|
203 |
158 202
|
syl |
|
204 |
113 203
|
ffvelrnd |
|
205 |
154 204
|
sseldd |
|
206 |
|
elicc2 |
|
207 |
5 6 206
|
syl2anc |
|
208 |
205 207
|
mpbid |
|
209 |
208
|
simp3d |
|
210 |
|
prid2g |
|
211 |
|
elun1 |
|
212 |
6 210 211
|
3syl |
|
213 |
212 9
|
eleqtrrdi |
|
214 |
|
eqeq1 |
|
215 |
|
eqcom |
|
216 |
214 215
|
syl6bb |
|
217 |
216
|
rexbidv |
|
218 |
217
|
rspcv |
|
219 |
213 126 218
|
sylc |
|
220 |
215
|
biimpri |
|
221 |
220
|
3ad2ant3 |
|
222 |
114
|
ffvelrnda |
|
223 |
104 205
|
sseldd |
|
224 |
223
|
adantr |
|
225 |
169
|
adantl |
|
226 |
|
elfzel2 |
|
227 |
226
|
zred |
|
228 |
227
|
adantl |
|
229 |
|
elfzle2 |
|
230 |
229
|
adantl |
|
231 |
225 228 230
|
lensymd |
|
232 |
|
breq1 |
|
233 |
|
fveq2 |
|
234 |
233
|
breq1d |
|
235 |
232 234
|
bibi12d |
|
236 |
235
|
ralbidv |
|
237 |
236
|
rspcv |
|
238 |
203 179 237
|
sylc |
|
239 |
238
|
r19.21bi |
|
240 |
231 239
|
mtbid |
|
241 |
222 224 240
|
nltled |
|
242 |
241
|
3adant3 |
|
243 |
221 242
|
eqbrtrd |
|
244 |
243
|
rexlimdv3a |
|
245 |
219 244
|
mpd |
|
246 |
223 6
|
letri3d |
|
247 |
209 245 246
|
mpbir2and |
|
248 |
|
elfzoelz |
|
249 |
248
|
zred |
|
250 |
249
|
ltp1d |
|
251 |
250
|
adantl |
|
252 |
179
|
adantr |
|
253 |
|
elfzofz |
|
254 |
253
|
adantl |
|
255 |
|
fzofzp1 |
|
256 |
255
|
adantl |
|
257 |
|
breq1 |
|
258 |
|
fveq2 |
|
259 |
258
|
breq1d |
|
260 |
257 259
|
bibi12d |
|
261 |
|
breq2 |
|
262 |
|
fveq2 |
|
263 |
262
|
breq2d |
|
264 |
261 263
|
bibi12d |
|
265 |
260 264
|
rspc2v |
|
266 |
254 256 265
|
syl2anc |
|
267 |
252 266
|
mpd |
|
268 |
251 267
|
mpbid |
|
269 |
268
|
ralrimiva |
|
270 |
201 247 269
|
jca31 |
|
271 |
8
|
fourierdlem2 |
|
272 |
99 271
|
syl |
|
273 |
120 270 272
|
mpbir2and |
|
274 |
99 273 108
|
jca31 |
|