Step |
Hyp |
Ref |
Expression |
1 |
|
bdayelon |
|
2 |
|
bdayelon |
|
3 |
|
naddcl |
|
4 |
1 2 3
|
mp2an |
|
5 |
|
bdayelon |
|
6 |
|
bdayelon |
|
7 |
|
naddcl |
|
8 |
5 6 7
|
mp2an |
|
9 |
|
bdayelon |
|
10 |
|
bdayelon |
|
11 |
|
naddcl |
|
12 |
9 10 11
|
mp2an |
|
13 |
8 12
|
onun2i |
|
14 |
|
naddcl |
|
15 |
5 10 14
|
mp2an |
|
16 |
|
naddcl |
|
17 |
9 6 16
|
mp2an |
|
18 |
15 17
|
onun2i |
|
19 |
13 18
|
onun2i |
|
20 |
4 19
|
onun2i |
|
21 |
|
risset |
|
22 |
20 21
|
mpbi |
|
23 |
|
fveq2 |
|
24 |
23
|
oveq1d |
|
25 |
24
|
uneq1d |
|
26 |
25
|
eqeq2d |
|
27 |
|
oveq1 |
|
28 |
27
|
eleq1d |
|
29 |
28
|
anbi1d |
|
30 |
26 29
|
imbi12d |
|
31 |
|
fveq2 |
|
32 |
31
|
oveq2d |
|
33 |
32
|
uneq1d |
|
34 |
33
|
eqeq2d |
|
35 |
|
oveq2 |
|
36 |
35
|
eleq1d |
|
37 |
36
|
anbi1d |
|
38 |
34 37
|
imbi12d |
|
39 |
|
fveq2 |
|
40 |
39
|
oveq1d |
|
41 |
40
|
uneq1d |
|
42 |
39
|
oveq1d |
|
43 |
42
|
uneq1d |
|
44 |
41 43
|
uneq12d |
|
45 |
44
|
uneq2d |
|
46 |
45
|
eqeq2d |
|
47 |
|
breq1 |
|
48 |
47
|
anbi1d |
|
49 |
|
oveq1 |
|
50 |
|
oveq1 |
|
51 |
49 50
|
oveq12d |
|
52 |
51
|
breq1d |
|
53 |
48 52
|
imbi12d |
|
54 |
53
|
anbi2d |
|
55 |
46 54
|
imbi12d |
|
56 |
|
fveq2 |
|
57 |
56
|
oveq1d |
|
58 |
57
|
uneq2d |
|
59 |
56
|
oveq1d |
|
60 |
59
|
uneq2d |
|
61 |
58 60
|
uneq12d |
|
62 |
61
|
uneq2d |
|
63 |
62
|
eqeq2d |
|
64 |
|
breq2 |
|
65 |
64
|
anbi1d |
|
66 |
|
oveq1 |
|
67 |
|
oveq1 |
|
68 |
66 67
|
oveq12d |
|
69 |
68
|
breq2d |
|
70 |
65 69
|
imbi12d |
|
71 |
70
|
anbi2d |
|
72 |
63 71
|
imbi12d |
|
73 |
|
fveq2 |
|
74 |
73
|
oveq2d |
|
75 |
74
|
uneq1d |
|
76 |
73
|
oveq2d |
|
77 |
76
|
uneq2d |
|
78 |
75 77
|
uneq12d |
|
79 |
78
|
uneq2d |
|
80 |
79
|
eqeq2d |
|
81 |
|
breq1 |
|
82 |
81
|
anbi2d |
|
83 |
|
oveq2 |
|
84 |
83
|
oveq2d |
|
85 |
|
oveq2 |
|
86 |
85
|
oveq2d |
|
87 |
84 86
|
breq12d |
|
88 |
82 87
|
imbi12d |
|
89 |
88
|
anbi2d |
|
90 |
80 89
|
imbi12d |
|
91 |
|
fveq2 |
|
92 |
91
|
oveq2d |
|
93 |
92
|
uneq2d |
|
94 |
91
|
oveq2d |
|
95 |
94
|
uneq1d |
|
96 |
93 95
|
uneq12d |
|
97 |
96
|
uneq2d |
|
98 |
97
|
eqeq2d |
|
99 |
|
breq2 |
|
100 |
99
|
anbi2d |
|
101 |
|
oveq2 |
|
102 |
101
|
oveq1d |
|
103 |
|
oveq2 |
|
104 |
103
|
oveq1d |
|
105 |
102 104
|
breq12d |
|
106 |
100 105
|
imbi12d |
|
107 |
106
|
anbi2d |
|
108 |
98 107
|
imbi12d |
|
109 |
30 38 55 72 90 108
|
cbvral6vw |
|
110 |
|
eqeq1 |
|
111 |
110
|
imbi1d |
|
112 |
111
|
6ralbidv |
|
113 |
109 112
|
bitr3id |
|
114 |
|
raleq |
|
115 |
|
ralrot3 |
|
116 |
|
ralrot3 |
|
117 |
|
ralrot3 |
|
118 |
|
r19.23v |
|
119 |
|
risset |
|
120 |
119
|
imbi1i |
|
121 |
118 120
|
bitr4i |
|
122 |
121
|
2ralbii |
|
123 |
117 122
|
bitr3i |
|
124 |
123
|
2ralbii |
|
125 |
116 124
|
bitr3i |
|
126 |
125
|
2ralbii |
|
127 |
115 126
|
bitr3i |
|
128 |
114 127
|
bitrdi |
|
129 |
|
simpl |
|
130 |
|
simprl1 |
|
131 |
|
simprl2 |
|
132 |
129 130 131
|
mulsproplem11 |
|
133 |
129
|
adantr |
|
134 |
|
simprl3 |
|
135 |
134
|
adantr |
|
136 |
|
simprr1 |
|
137 |
136
|
adantr |
|
138 |
|
simprr2 |
|
139 |
138
|
adantr |
|
140 |
|
simprr3 |
|
141 |
140
|
adantr |
|
142 |
|
simprl |
|
143 |
|
simprr |
|
144 |
133 135 137 139 141 142 143
|
mulsproplem14 |
|
145 |
144
|
ex |
|
146 |
132 145
|
jca |
|
147 |
146
|
ex |
|
148 |
128 147
|
biimtrdi |
|
149 |
148
|
impd |
|
150 |
149
|
com12 |
|
151 |
150
|
anassrs |
|
152 |
151
|
ralrimivvva |
|
153 |
152
|
ralrimivvva |
|
154 |
153
|
a1i |
|
155 |
113 154
|
tfis2 |
|
156 |
|
fveq2 |
|
157 |
156
|
oveq1d |
|
158 |
157
|
uneq1d |
|
159 |
158
|
eqeq2d |
|
160 |
|
oveq1 |
|
161 |
160
|
eleq1d |
|
162 |
161
|
anbi1d |
|
163 |
159 162
|
imbi12d |
|
164 |
|
fveq2 |
|
165 |
164
|
oveq2d |
|
166 |
165
|
uneq1d |
|
167 |
166
|
eqeq2d |
|
168 |
|
oveq2 |
|
169 |
168
|
eleq1d |
|
170 |
169
|
anbi1d |
|
171 |
167 170
|
imbi12d |
|
172 |
|
fveq2 |
|
173 |
172
|
oveq1d |
|
174 |
173
|
uneq1d |
|
175 |
172
|
oveq1d |
|
176 |
175
|
uneq1d |
|
177 |
174 176
|
uneq12d |
|
178 |
177
|
uneq2d |
|
179 |
178
|
eqeq2d |
|
180 |
|
breq1 |
|
181 |
180
|
anbi1d |
|
182 |
|
oveq1 |
|
183 |
|
oveq1 |
|
184 |
182 183
|
oveq12d |
|
185 |
184
|
breq1d |
|
186 |
181 185
|
imbi12d |
|
187 |
186
|
anbi2d |
|
188 |
179 187
|
imbi12d |
|
189 |
|
fveq2 |
|
190 |
189
|
oveq1d |
|
191 |
190
|
uneq2d |
|
192 |
189
|
oveq1d |
|
193 |
192
|
uneq2d |
|
194 |
191 193
|
uneq12d |
|
195 |
194
|
uneq2d |
|
196 |
195
|
eqeq2d |
|
197 |
|
breq2 |
|
198 |
197
|
anbi1d |
|
199 |
|
oveq1 |
|
200 |
|
oveq1 |
|
201 |
199 200
|
oveq12d |
|
202 |
201
|
breq2d |
|
203 |
198 202
|
imbi12d |
|
204 |
203
|
anbi2d |
|
205 |
196 204
|
imbi12d |
|
206 |
|
fveq2 |
|
207 |
206
|
oveq2d |
|
208 |
207
|
uneq1d |
|
209 |
206
|
oveq2d |
|
210 |
209
|
uneq2d |
|
211 |
208 210
|
uneq12d |
|
212 |
211
|
uneq2d |
|
213 |
212
|
eqeq2d |
|
214 |
|
breq1 |
|
215 |
214
|
anbi2d |
|
216 |
|
oveq2 |
|
217 |
216
|
oveq2d |
|
218 |
|
oveq2 |
|
219 |
218
|
oveq2d |
|
220 |
217 219
|
breq12d |
|
221 |
215 220
|
imbi12d |
|
222 |
221
|
anbi2d |
|
223 |
213 222
|
imbi12d |
|
224 |
|
fveq2 |
|
225 |
224
|
oveq2d |
|
226 |
225
|
uneq2d |
|
227 |
224
|
oveq2d |
|
228 |
227
|
uneq1d |
|
229 |
226 228
|
uneq12d |
|
230 |
229
|
uneq2d |
|
231 |
230
|
eqeq2d |
|
232 |
|
breq2 |
|
233 |
232
|
anbi2d |
|
234 |
|
oveq2 |
|
235 |
234
|
oveq1d |
|
236 |
|
oveq2 |
|
237 |
236
|
oveq1d |
|
238 |
235 237
|
breq12d |
|
239 |
233 238
|
imbi12d |
|
240 |
239
|
anbi2d |
|
241 |
231 240
|
imbi12d |
|
242 |
163 171 188 205 223 241
|
rspc6v |
|
243 |
155 242
|
syl5com |
|
244 |
243
|
com23 |
|
245 |
244
|
rexlimiv |
|
246 |
22 245
|
ax-mp |
|