Step |
Hyp |
Ref |
Expression |
1 |
|
eulerpart.p |
|
2 |
|
eulerpart.o |
|
3 |
|
eulerpart.d |
|
4 |
|
eulerpart.j |
|
5 |
|
eulerpart.f |
|
6 |
|
eulerpart.h |
|
7 |
|
eulerpart.m |
|
8 |
|
eulerpart.r |
|
9 |
|
eulerpart.t |
|
10 |
|
eulerpart.g |
|
11 |
1 2 3 4 5 6 7 8 9 10
|
eulerpartlemgv |
|
12 |
11
|
fveq1d |
|
13 |
12
|
adantr |
|
14 |
|
nnex |
|
15 |
|
imassrn |
|
16 |
4 5
|
oddpwdc |
|
17 |
|
f1of |
|
18 |
|
frn |
|
19 |
16 17 18
|
mp2b |
|
20 |
15 19
|
sstri |
|
21 |
|
simpr |
|
22 |
|
indfval |
|
23 |
14 20 21 22
|
mp3an12i |
|
24 |
|
ffn |
|
25 |
16 17 24
|
mp2b |
|
26 |
1 2 3 4 5 6 7 8 9 10
|
eulerpartlemmf |
|
27 |
1 2 3 4 5 6 7
|
eulerpartlem1 |
|
28 |
|
f1of |
|
29 |
27 28
|
ax-mp |
|
30 |
29
|
ffvelrni |
|
31 |
26 30
|
syl |
|
32 |
31
|
elin1d |
|
33 |
32
|
adantr |
|
34 |
33
|
elpwid |
|
35 |
|
fvelimab |
|
36 |
25 34 35
|
sylancr |
|
37 |
4
|
ssrab3 |
|
38 |
|
fveq1 |
|
39 |
38
|
eleq2d |
|
40 |
39
|
anbi2d |
|
41 |
40
|
opabbidv |
|
42 |
14 37
|
ssexi |
|
43 |
|
abid2 |
|
44 |
43
|
fvexi |
|
45 |
44
|
a1i |
|
46 |
42 45
|
opabex3 |
|
47 |
46
|
a1i |
|
48 |
7 41 26 47
|
fvmptd3 |
|
49 |
|
simpl |
|
50 |
49
|
eleq1d |
|
51 |
|
simpr |
|
52 |
49
|
fveq2d |
|
53 |
51 52
|
eleq12d |
|
54 |
50 53
|
anbi12d |
|
55 |
54
|
cbvopabv |
|
56 |
48 55
|
eqtrdi |
|
57 |
56
|
eleq2d |
|
58 |
1 2 3 4 5 6 7 8 9
|
eulerpartlemt0 |
|
59 |
58
|
simp1bi |
|
60 |
|
nn0ex |
|
61 |
60 14
|
elmap |
|
62 |
59 61
|
sylib |
|
63 |
|
ffun |
|
64 |
|
funres |
|
65 |
62 63 64
|
3syl |
|
66 |
|
fssres |
|
67 |
62 37 66
|
sylancl |
|
68 |
|
fdm |
|
69 |
68
|
eleq2d |
|
70 |
67 69
|
syl |
|
71 |
70
|
biimpar |
|
72 |
|
fvco |
|
73 |
65 71 72
|
syl2an2r |
|
74 |
|
fvres |
|
75 |
74
|
fveq2d |
|
76 |
75
|
adantl |
|
77 |
73 76
|
eqtrd |
|
78 |
77
|
eleq2d |
|
79 |
78
|
pm5.32da |
|
80 |
79
|
opabbidv |
|
81 |
80
|
eleq2d |
|
82 |
|
elopab |
|
83 |
81 82
|
syl6bb |
|
84 |
|
ancom |
|
85 |
|
anass |
|
86 |
84 85
|
bitri |
|
87 |
86
|
2exbii |
|
88 |
|
df-rex |
|
89 |
88
|
anbi2i |
|
90 |
89
|
exbii |
|
91 |
|
df-rex |
|
92 |
|
exdistr |
|
93 |
90 91 92
|
3bitr4i |
|
94 |
87 93
|
bitr4i |
|
95 |
83 94
|
syl6bb |
|
96 |
57 95
|
bitrd |
|
97 |
96
|
biimpa |
|
98 |
97
|
adantlr |
|
99 |
|
fveq2 |
|
100 |
99
|
adantl |
|
101 |
|
bitsss |
|
102 |
101
|
sseli |
|
103 |
102
|
anim2i |
|
104 |
103
|
ad2antlr |
|
105 |
|
opelxp |
|
106 |
4 5
|
oddpwdcv |
|
107 |
|
vex |
|
108 |
|
vex |
|
109 |
107 108
|
op2nd |
|
110 |
109
|
oveq2i |
|
111 |
107 108
|
op1st |
|
112 |
110 111
|
oveq12i |
|
113 |
106 112
|
eqtrdi |
|
114 |
105 113
|
sylbir |
|
115 |
104 114
|
syl |
|
116 |
100 115
|
eqtr2d |
|
117 |
116
|
ex |
|
118 |
117
|
reximdvva |
|
119 |
98 118
|
mpd |
|
120 |
|
ssrexv |
|
121 |
37 119 120
|
mpsyl |
|
122 |
121
|
adantr |
|
123 |
|
eqeq2 |
|
124 |
123
|
rexbidv |
|
125 |
124
|
adantl |
|
126 |
125
|
rexbidv |
|
127 |
122 126
|
mpbid |
|
128 |
127
|
r19.29an |
|
129 |
|
simp-5l |
|
130 |
|
simpllr |
|
131 |
|
simplr |
|
132 |
68
|
eleq2d |
|
133 |
67 132
|
syl |
|
134 |
133
|
biimpar |
|
135 |
|
fvco |
|
136 |
65 134 135
|
syl2an2r |
|
137 |
|
fvres |
|
138 |
137
|
fveq2d |
|
139 |
138
|
adantl |
|
140 |
136 139
|
eqtrd |
|
141 |
129 130 140
|
syl2anc |
|
142 |
131 141
|
eleqtrrd |
|
143 |
48
|
eleq2d |
|
144 |
|
opabidw |
|
145 |
143 144
|
syl6bb |
|
146 |
145
|
biimpar |
|
147 |
129 130 142 146
|
syl12anc |
|
148 |
|
simpr |
|
149 |
34
|
ad4antr |
|
150 |
149 147
|
sseldd |
|
151 |
|
opeq1 |
|
152 |
151
|
eleq1d |
|
153 |
151
|
fveq2d |
|
154 |
|
oveq2 |
|
155 |
153 154
|
eqeq12d |
|
156 |
152 155
|
imbi12d |
|
157 |
|
opeq2 |
|
158 |
157
|
eleq1d |
|
159 |
157
|
fveq2d |
|
160 |
|
oveq2 |
|
161 |
160
|
oveq1d |
|
162 |
159 161
|
eqeq12d |
|
163 |
158 162
|
imbi12d |
|
164 |
163 113
|
chvarvv |
|
165 |
156 164
|
chvarvv |
|
166 |
|
eqeq2 |
|
167 |
166
|
biimpa |
|
168 |
165 167
|
sylan2 |
|
169 |
148 150 168
|
syl2anc |
|
170 |
|
fveqeq2 |
|
171 |
170
|
rspcev |
|
172 |
147 169 171
|
syl2anc |
|
173 |
|
oveq2 |
|
174 |
173
|
eqeq1d |
|
175 |
160
|
oveq1d |
|
176 |
175
|
eqeq1d |
|
177 |
174 176
|
sylan9bb |
|
178 |
|
simpl |
|
179 |
178
|
fveq2d |
|
180 |
179
|
fveq2d |
|
181 |
177 180
|
cbvrexdva2 |
|
182 |
181
|
cbvrexvw |
|
183 |
|
nfv |
|
184 |
|
nfv |
|
185 |
|
nfre1 |
|
186 |
184 185
|
nfan |
|
187 |
183 186
|
nfan |
|
188 |
|
simplr |
|
189 |
62
|
ffvelrnda |
|
190 |
189
|
adantr |
|
191 |
|
elnn0 |
|
192 |
190 191
|
sylib |
|
193 |
|
n0i |
|
194 |
193
|
adantl |
|
195 |
|
fveq2 |
|
196 |
|
0bits |
|
197 |
195 196
|
eqtrdi |
|
198 |
194 197
|
nsyl |
|
199 |
192 198
|
olcnd |
|
200 |
58
|
simp3bi |
|
201 |
200
|
sselda |
|
202 |
|
breq2 |
|
203 |
202
|
notbid |
|
204 |
203 4
|
elrab2 |
|
205 |
204
|
simprbi |
|
206 |
201 205
|
syl |
|
207 |
206
|
ralrimiva |
|
208 |
|
ffn |
|
209 |
|
elpreima |
|
210 |
62 208 209
|
3syl |
|
211 |
210
|
imbi1d |
|
212 |
|
impexp |
|
213 |
211 212
|
syl6bb |
|
214 |
213
|
ralbidv2 |
|
215 |
207 214
|
mpbid |
|
216 |
|
fveq2 |
|
217 |
216
|
eleq1d |
|
218 |
|
breq2 |
|
219 |
218
|
notbid |
|
220 |
217 219
|
imbi12d |
|
221 |
220
|
cbvralvw |
|
222 |
215 221
|
sylibr |
|
223 |
222
|
r19.21bi |
|
224 |
223
|
imp |
|
225 |
199 224
|
syldan |
|
226 |
|
breq2 |
|
227 |
226
|
notbid |
|
228 |
227 4
|
elrab2 |
|
229 |
188 225 228
|
sylanbrc |
|
230 |
229
|
adantlrr |
|
231 |
230
|
adantr |
|
232 |
|
simprr |
|
233 |
187 231 232
|
r19.29af |
|
234 |
233 232
|
jca |
|
235 |
234
|
ex |
|
236 |
235
|
reximdv2 |
|
237 |
236
|
imp |
|
238 |
237
|
adantlr |
|
239 |
182 238
|
sylan2b |
|
240 |
172 239
|
r19.29vva |
|
241 |
128 240
|
impbida |
|
242 |
36 241
|
bitrd |
|
243 |
242
|
ifbid |
|
244 |
13 23 243
|
3eqtrd |
|