Step |
Hyp |
Ref |
Expression |
1 |
|
esum2d.0 |
|
2 |
|
esum2d.1 |
|
3 |
|
esum2d.2 |
|
4 |
|
esum2d.3 |
|
5 |
|
esum2d.4 |
|
6 |
|
esum2dlem.e |
|
7 |
|
esumeq1 |
|
8 |
|
nfv |
|
9 |
|
iuneq1 |
|
10 |
8 9
|
esumeq1d |
|
11 |
7 10
|
eqeq12d |
|
12 |
|
esumeq1 |
|
13 |
|
nfv |
|
14 |
|
iuneq1 |
|
15 |
13 14
|
esumeq1d |
|
16 |
12 15
|
eqeq12d |
|
17 |
|
esumeq1 |
|
18 |
|
nfv |
|
19 |
|
iuneq1 |
|
20 |
18 19
|
esumeq1d |
|
21 |
17 20
|
eqeq12d |
|
22 |
|
esumeq1 |
|
23 |
|
nfv |
|
24 |
|
iuneq1 |
|
25 |
23 24
|
esumeq1d |
|
26 |
22 25
|
eqeq12d |
|
27 |
|
esumnul |
|
28 |
|
0iun |
|
29 |
|
esumeq1 |
|
30 |
28 29
|
ax-mp |
|
31 |
|
esumnul |
|
32 |
27 30 31
|
3eqtr4ri |
|
33 |
32
|
a1i |
|
34 |
|
simpr |
|
35 |
|
nfcsb1v |
|
36 |
|
nfcsb1v |
|
37 |
35 36
|
nfesum2 |
|
38 |
|
csbeq1a |
|
39 |
|
csbeq1a |
|
40 |
38 39
|
esumeq12d |
|
41 |
40
|
adantl |
|
42 |
|
simprr |
|
43 |
42
|
eldifad |
|
44 |
4
|
adantlr |
|
45 |
44
|
ralrimiva |
|
46 |
|
rspcsbela |
|
47 |
43 45 46
|
syl2anc |
|
48 |
|
simpll |
|
49 |
43
|
adantr |
|
50 |
|
simpr |
|
51 |
5
|
ex |
|
52 |
51
|
sbcimdv |
|
53 |
|
sbcan |
|
54 |
|
sbcel1v |
|
55 |
|
sbcel2 |
|
56 |
54 55
|
anbi12i |
|
57 |
53 56
|
bitri |
|
58 |
|
vex |
|
59 |
|
sbcel1g |
|
60 |
58 59
|
ax-mp |
|
61 |
52 57 60
|
3imtr3g |
|
62 |
61
|
imp |
|
63 |
48 49 50 62
|
syl12anc |
|
64 |
63
|
ralrimiva |
|
65 |
|
nfcv |
|
66 |
65
|
esumcl |
|
67 |
47 64 66
|
syl2anc |
|
68 |
37 41 42 67
|
esumsnf |
|
69 |
|
nfv |
|
70 |
|
nfv |
|
71 |
36
|
nfeq2 |
|
72 |
70 71
|
nfim |
|
73 |
|
opeq1 |
|
74 |
73
|
eqeq2d |
|
75 |
39
|
eqeq2d |
|
76 |
74 75
|
imbi12d |
|
77 |
72 76 2
|
chvarfv |
|
78 |
|
vsnid |
|
79 |
78
|
a1i |
|
80 |
|
simpr |
|
81 |
79 80
|
opelxpd |
|
82 |
|
xp2nd |
|
83 |
|
xp1st |
|
84 |
|
fvex |
|
85 |
84
|
elsn |
|
86 |
83 85
|
sylib |
|
87 |
|
eqop |
|
88 |
86 87
|
mpbirand |
|
89 |
|
eqcom |
|
90 |
88 89
|
syl6bb |
|
91 |
90
|
ad2antlr |
|
92 |
91
|
ralrimiva |
|
93 |
|
reu6i |
|
94 |
82 92 93
|
syl2an2 |
|
95 |
81 94
|
f1mptrn |
|
96 |
95
|
ex |
|
97 |
96
|
sbcimdv |
|
98 |
|
sbcfung |
|
99 |
|
csbcnv |
|
100 |
|
csbmpt12 |
|
101 |
|
csbopg |
|
102 |
|
csbvarg |
|
103 |
|
csbconstg |
|
104 |
102 103
|
opeq12d |
|
105 |
101 104
|
eqtrd |
|
106 |
105
|
mpteq2dv |
|
107 |
100 106
|
eqtrd |
|
108 |
107
|
cnveqd |
|
109 |
99 108
|
syl5eqr |
|
110 |
109
|
funeqd |
|
111 |
98 110
|
bitrd |
|
112 |
58 111
|
ax-mp |
|
113 |
97 54 112
|
3imtr3g |
|
114 |
113
|
imp |
|
115 |
43 114
|
syldan |
|
116 |
|
vsnid |
|
117 |
116
|
a1i |
|
118 |
117 50
|
opelxpd |
|
119 |
1 69 65 77 47 115 63 118
|
esumc |
|
120 |
|
nfab1 |
|
121 |
|
nfcv |
|
122 |
|
opeq1 |
|
123 |
122
|
eqeq2d |
|
124 |
123
|
rexbidv |
|
125 |
58 124
|
rexsn |
|
126 |
|
elxp2 |
|
127 |
|
abid |
|
128 |
125 126 127
|
3bitr4ri |
|
129 |
120 121 128
|
eqri |
|
130 |
|
esumeq1 |
|
131 |
129 130
|
ax-mp |
|
132 |
119 131
|
eqtrdi |
|
133 |
68 132
|
eqtrd |
|
134 |
133
|
adantr |
|
135 |
34 134
|
oveq12d |
|
136 |
|
nfv |
|
137 |
|
nfcv |
|
138 |
|
nfcv |
|
139 |
|
vex |
|
140 |
139
|
a1i |
|
141 |
|
snex |
|
142 |
141
|
a1i |
|
143 |
42
|
eldifbd |
|
144 |
|
disjsn |
|
145 |
143 144
|
sylibr |
|
146 |
|
simpll |
|
147 |
|
simprl |
|
148 |
147
|
sselda |
|
149 |
5
|
anassrs |
|
150 |
149
|
ralrimiva |
|
151 |
|
nfcv |
|
152 |
151
|
esumcl |
|
153 |
4 150 152
|
syl2anc |
|
154 |
146 148 153
|
syl2anc |
|
155 |
|
simpll |
|
156 |
43
|
snssd |
|
157 |
156
|
sselda |
|
158 |
155 157 153
|
syl2anc |
|
159 |
136 137 138 140 142 145 154 158
|
esumsplit |
|
160 |
159
|
adantr |
|
161 |
|
iunxun |
|
162 |
138 35
|
nfxp |
|
163 |
|
sneq |
|
164 |
163 38
|
xpeq12d |
|
165 |
162 164
|
iunxsngf |
|
166 |
58 165
|
ax-mp |
|
167 |
166
|
uneq2i |
|
168 |
161 167
|
eqtri |
|
169 |
|
esumeq1 |
|
170 |
168 169
|
ax-mp |
|
171 |
|
nfv |
|
172 |
|
nfcv |
|
173 |
|
nfcv |
|
174 |
|
snex |
|
175 |
148 44
|
syldan |
|
176 |
|
xpexg |
|
177 |
174 175 176
|
sylancr |
|
178 |
177
|
ralrimiva |
|
179 |
|
iunexg |
|
180 |
139 178 179
|
sylancr |
|
181 |
|
xpexg |
|
182 |
141 47 181
|
sylancr |
|
183 |
|
simpr |
|
184 |
143
|
adantr |
|
185 |
|
nelne2 |
|
186 |
183 184 185
|
syl2anc |
|
187 |
|
disjsn2 |
|
188 |
|
xpdisj1 |
|
189 |
186 187 188
|
3syl |
|
190 |
189
|
iuneq2dv |
|
191 |
162
|
iunin1f |
|
192 |
|
iun0 |
|
193 |
190 191 192
|
3eqtr3g |
|
194 |
|
simpll |
|
195 |
|
iunss1 |
|
196 |
147 195
|
syl |
|
197 |
196
|
sselda |
|
198 |
|
nfv |
|
199 |
|
nfiu1 |
|
200 |
199
|
nfcri |
|
201 |
198 200
|
nfan |
|
202 |
|
nfv |
|
203 |
|
nfcv |
|
204 |
1 203
|
nfel |
|
205 |
2
|
adantl |
|
206 |
|
simp-5l |
|
207 |
|
simp-4r |
|
208 |
|
simplr |
|
209 |
206 207 208 5
|
syl12anc |
|
210 |
205 209
|
eqeltrd |
|
211 |
|
elsnxp |
|
212 |
211
|
biimpa |
|
213 |
212
|
adantll |
|
214 |
202 204 210 213
|
r19.29af2 |
|
215 |
|
simpr |
|
216 |
|
eliun |
|
217 |
215 216
|
sylib |
|
218 |
201 214 217
|
r19.29af |
|
219 |
194 197 218
|
syl2anc |
|
220 |
|
simpll |
|
221 |
|
nfcv |
|
222 |
|
nfcv |
|
223 |
221 222 162 164
|
ssiun2sf |
|
224 |
43 223
|
syl |
|
225 |
224
|
sselda |
|
226 |
220 225 218
|
syl2anc |
|
227 |
171 172 173 180 182 193 219 226
|
esumsplit |
|
228 |
170 227
|
syl5eq |
|
229 |
228
|
adantr |
|
230 |
135 160 229
|
3eqtr4d |
|
231 |
230
|
ex |
|
232 |
11 16 21 26 33 231 6
|
findcard2d |
|