Step |
Hyp |
Ref |
Expression |
1 |
|
sge0iunmptlemfi.a |
|
2 |
|
sge0iunmptlemfi.b |
|
3 |
|
sge0iunmptlemfi.dj |
|
4 |
|
sge0iunmptlemfi.c |
|
5 |
|
sge0iunmptlemfi.re |
|
6 |
|
iuneq1 |
|
7 |
6
|
mpteq1d |
|
8 |
7
|
fveq2d |
|
9 |
|
mpteq1 |
|
10 |
9
|
fveq2d |
|
11 |
8 10
|
eqeq12d |
|
12 |
|
iuneq1 |
|
13 |
12
|
mpteq1d |
|
14 |
13
|
fveq2d |
|
15 |
|
mpteq1 |
|
16 |
15
|
fveq2d |
|
17 |
14 16
|
eqeq12d |
|
18 |
|
iuneq1 |
|
19 |
18
|
mpteq1d |
|
20 |
19
|
fveq2d |
|
21 |
|
mpteq1 |
|
22 |
21
|
fveq2d |
|
23 |
20 22
|
eqeq12d |
|
24 |
|
iuneq1 |
|
25 |
24
|
mpteq1d |
|
26 |
25
|
fveq2d |
|
27 |
|
mpteq1 |
|
28 |
27
|
fveq2d |
|
29 |
26 28
|
eqeq12d |
|
30 |
|
0iun |
|
31 |
|
mpteq1 |
|
32 |
30 31
|
ax-mp |
|
33 |
|
mpt0 |
|
34 |
32 33
|
eqtri |
|
35 |
34
|
fveq2i |
|
36 |
|
mpt0 |
|
37 |
36
|
fveq2i |
|
38 |
35 37
|
eqtr4i |
|
39 |
38
|
a1i |
|
40 |
|
nfv |
|
41 |
|
nfcv |
|
42 |
|
nfiu1 |
|
43 |
|
nfcv |
|
44 |
42 43
|
nfmpt |
|
45 |
41 44
|
nffv |
|
46 |
|
simprl |
|
47 |
1
|
adantr |
|
48 |
|
simpr |
|
49 |
|
ssfi |
|
50 |
47 48 49
|
syl2anc |
|
51 |
46 50
|
syldan |
|
52 |
|
simprr |
|
53 |
|
eldifn |
|
54 |
|
disjsn |
|
55 |
53 54
|
sylibr |
|
56 |
55
|
adantl |
|
57 |
56
|
adantl |
|
58 |
57 54
|
sylib |
|
59 |
|
simpll |
|
60 |
|
ssel2 |
|
61 |
60
|
adantll |
|
62 |
59 61 5
|
syl2anc |
|
63 |
62
|
recnd |
|
64 |
63
|
adantlrr |
|
65 |
|
csbeq1a |
|
66 |
|
nfcsb1v |
|
67 |
|
vex |
|
68 |
66 67 65
|
iunxsnf |
|
69 |
65 68
|
eqtr4di |
|
70 |
69
|
mpteq1d |
|
71 |
70
|
fveq2d |
|
72 |
68
|
mpteq1i |
|
73 |
72
|
a1i |
|
74 |
73
|
fveq2d |
|
75 |
|
eldifi |
|
76 |
|
nfv |
|
77 |
66 43
|
nfmpt |
|
78 |
41 77
|
nffv |
|
79 |
|
nfcv |
|
80 |
78 79
|
nfel |
|
81 |
76 80
|
nfim |
|
82 |
|
eleq1w |
|
83 |
82
|
anbi2d |
|
84 |
70 72
|
eqtrdi |
|
85 |
84
|
fveq2d |
|
86 |
85
|
eleq1d |
|
87 |
83 86
|
imbi12d |
|
88 |
81 87 5
|
chvarfv |
|
89 |
75 88
|
sylan2 |
|
90 |
74 89
|
eqeltrd |
|
91 |
90
|
adantrl |
|
92 |
91
|
recnd |
|
93 |
40 45 51 52 58 64 71 92
|
fsumsplitsn |
|
94 |
93
|
eqcomd |
|
95 |
94
|
adantr |
|
96 |
|
iunxun |
|
97 |
96
|
mpteq1i |
|
98 |
97
|
fveq2i |
|
99 |
98
|
a1i |
|
100 |
|
nfv |
|
101 |
2
|
ralrimiva |
|
102 |
|
iunexg |
|
103 |
1 101 102
|
syl2anc |
|
104 |
103
|
adantr |
|
105 |
|
iunss1 |
|
106 |
105
|
adantl |
|
107 |
104 106
|
ssexd |
|
108 |
107
|
adantrr |
|
109 |
103
|
adantr |
|
110 |
|
snssi |
|
111 |
75 110
|
syl |
|
112 |
|
iunss1 |
|
113 |
111 112
|
syl |
|
114 |
113
|
adantl |
|
115 |
109 114
|
ssexd |
|
116 |
115
|
adantrl |
|
117 |
3
|
adantr |
|
118 |
111
|
ad2antll |
|
119 |
|
disjiun |
|
120 |
117 46 118 57 119
|
syl13anc |
|
121 |
|
eliun |
|
122 |
121
|
biimpi |
|
123 |
122
|
adantl |
|
124 |
|
simp1l |
|
125 |
61
|
3adant3 |
|
126 |
|
simp3 |
|
127 |
124 125 126 4
|
syl3anc |
|
128 |
127
|
3exp |
|
129 |
128
|
rexlimdv |
|
130 |
129
|
adantr |
|
131 |
123 130
|
mpd |
|
132 |
131
|
adantlrr |
|
133 |
|
eliun |
|
134 |
133
|
biimpi |
|
135 |
134
|
adantl |
|
136 |
|
simp1l |
|
137 |
111
|
sselda |
|
138 |
137
|
adantll |
|
139 |
138
|
3adant3 |
|
140 |
|
simp3 |
|
141 |
136 139 140 4
|
syl3anc |
|
142 |
141
|
3exp |
|
143 |
142
|
rexlimdv |
|
144 |
143
|
adantr |
|
145 |
135 144
|
mpd |
|
146 |
145
|
adantlrl |
|
147 |
100 108 116 120 132 146
|
sge0splitmpt |
|
148 |
99 147
|
eqtrd |
|
149 |
148
|
adantr |
|
150 |
|
id |
|
151 |
150
|
adantl |
|
152 |
4
|
3expa |
|
153 |
|
eqid |
|
154 |
152 153
|
fmptd |
|
155 |
2 154
|
sge0ge0 |
|
156 |
5 155
|
jca |
|
157 |
|
elrege0 |
|
158 |
156 157
|
sylibr |
|
159 |
59 61 158
|
syl2anc |
|
160 |
|
eqid |
|
161 |
159 160
|
fmptd |
|
162 |
50 161
|
sge0fsum |
|
163 |
162
|
adantr |
|
164 |
|
fveq2 |
|
165 |
|
nfcv |
|
166 |
|
nfcv |
|
167 |
|
nfmpt1 |
|
168 |
|
nfcv |
|
169 |
167 168
|
nffv |
|
170 |
|
nfcv |
|
171 |
164 165 166 169 170
|
cbvsum |
|
172 |
171
|
a1i |
|
173 |
|
id |
|
174 |
|
fvexd |
|
175 |
160
|
fvmpt2 |
|
176 |
173 174 175
|
syl2anc |
|
177 |
176
|
adantl |
|
178 |
177
|
ralrimiva |
|
179 |
178
|
sumeq2d |
|
180 |
172 179
|
eqtrd |
|
181 |
180
|
adantr |
|
182 |
151 163 181
|
3eqtrd |
|
183 |
182
|
adantlrr |
|
184 |
183
|
oveq1d |
|
185 |
50 62
|
fsumrecl |
|
186 |
185
|
adantrr |
|
187 |
|
rexadd |
|
188 |
186 91 187
|
syl2anc |
|
189 |
188
|
adantr |
|
190 |
149 184 189
|
3eqtrd |
|
191 |
|
snfi |
|
192 |
191
|
a1i |
|
193 |
|
unfi |
|
194 |
51 192 193
|
syl2anc |
|
195 |
|
simpll |
|
196 |
60
|
ad4ant14 |
|
197 |
|
simpll |
|
198 |
|
elunnel1 |
|
199 |
|
elsni |
|
200 |
198 199
|
syl |
|
201 |
200
|
adantll |
|
202 |
|
simpr |
|
203 |
75
|
adantr |
|
204 |
202 203
|
eqeltrd |
|
205 |
197 201 204
|
syl2anc |
|
206 |
205
|
adantlll |
|
207 |
196 206
|
pm2.61dan |
|
208 |
207
|
adantll |
|
209 |
195 208 158
|
syl2anc |
|
210 |
194 209
|
sge0fsummpt |
|
211 |
210
|
adantr |
|
212 |
95 190 211
|
3eqtr4d |
|
213 |
212
|
ex |
|
214 |
11 17 23 29 39 213 1
|
findcard2d |
|