Step |
Hyp |
Ref |
Expression |
1 |
|
dvadd.f |
|
2 |
|
dvadd.x |
|
3 |
|
dvadd.g |
|
4 |
|
dvadd.y |
|
5 |
|
dvaddbr.s |
|
6 |
|
dvadd.bf |
|
7 |
|
dvadd.bg |
|
8 |
|
dvadd.j |
|
9 |
|
eqid |
|
10 |
|
eqid |
|
11 |
9 8 10 5 1 2
|
eldv |
|
12 |
6 11
|
mpbid |
|
13 |
12
|
simpld |
|
14 |
|
eqid |
|
15 |
9 8 14 5 3 4
|
eldv |
|
16 |
7 15
|
mpbid |
|
17 |
16
|
simpld |
|
18 |
13 17
|
elind |
|
19 |
8
|
cnfldtopon |
|
20 |
|
resttopon |
|
21 |
19 5 20
|
sylancr |
|
22 |
|
topontop |
|
23 |
21 22
|
syl |
|
24 |
|
toponuni |
|
25 |
21 24
|
syl |
|
26 |
2 25
|
sseqtrd |
|
27 |
4 25
|
sseqtrd |
|
28 |
|
eqid |
|
29 |
28
|
ntrin |
|
30 |
23 26 27 29
|
syl3anc |
|
31 |
18 30
|
eleqtrrd |
|
32 |
|
inss1 |
|
33 |
|
ssdif |
|
34 |
32 33
|
mp1i |
|
35 |
34
|
sselda |
|
36 |
2 5
|
sstrd |
|
37 |
28
|
ntrss2 |
|
38 |
23 26 37
|
syl2anc |
|
39 |
38 13
|
sseldd |
|
40 |
1 36 39
|
dvlem |
|
41 |
35 40
|
syldan |
|
42 |
|
inss2 |
|
43 |
|
ssdif |
|
44 |
42 43
|
mp1i |
|
45 |
44
|
sselda |
|
46 |
4 5
|
sstrd |
|
47 |
28
|
ntrss2 |
|
48 |
23 27 47
|
syl2anc |
|
49 |
48 17
|
sseldd |
|
50 |
3 46 49
|
dvlem |
|
51 |
45 50
|
syldan |
|
52 |
|
ssidd |
|
53 |
|
txtopon |
|
54 |
19 19 53
|
mp2an |
|
55 |
54
|
toponrestid |
|
56 |
12
|
simprd |
|
57 |
40
|
fmpttd |
|
58 |
36
|
ssdifssd |
|
59 |
|
eqid |
|
60 |
32 2
|
sstrid |
|
61 |
60 25
|
sseqtrd |
|
62 |
|
difssd |
|
63 |
61 62
|
unssd |
|
64 |
|
ssun1 |
|
65 |
64
|
a1i |
|
66 |
28
|
ntrss |
|
67 |
23 63 65 66
|
syl3anc |
|
68 |
67 31
|
sseldd |
|
69 |
68 39
|
elind |
|
70 |
32
|
a1i |
|
71 |
|
eqid |
|
72 |
28 71
|
restntr |
|
73 |
23 26 70 72
|
syl3anc |
|
74 |
8
|
cnfldtop |
|
75 |
74
|
a1i |
|
76 |
|
cnex |
|
77 |
|
ssexg |
|
78 |
5 76 77
|
sylancl |
|
79 |
|
restabs |
|
80 |
75 2 78 79
|
syl3anc |
|
81 |
80
|
fveq2d |
|
82 |
81
|
fveq1d |
|
83 |
73 82
|
eqtr3d |
|
84 |
69 83
|
eleqtrd |
|
85 |
|
undif1 |
|
86 |
39
|
snssd |
|
87 |
|
ssequn2 |
|
88 |
86 87
|
sylib |
|
89 |
85 88
|
eqtrid |
|
90 |
89
|
oveq2d |
|
91 |
90
|
fveq2d |
|
92 |
|
undif1 |
|
93 |
39 49
|
elind |
|
94 |
93
|
snssd |
|
95 |
|
ssequn2 |
|
96 |
94 95
|
sylib |
|
97 |
92 96
|
eqtrid |
|
98 |
91 97
|
fveq12d |
|
99 |
84 98
|
eleqtrrd |
|
100 |
57 34 58 8 59 99
|
limcres |
|
101 |
34
|
resmptd |
|
102 |
101
|
oveq1d |
|
103 |
100 102
|
eqtr3d |
|
104 |
56 103
|
eleqtrd |
|
105 |
16
|
simprd |
|
106 |
50
|
fmpttd |
|
107 |
46
|
ssdifssd |
|
108 |
|
eqid |
|
109 |
|
difssd |
|
110 |
61 109
|
unssd |
|
111 |
|
ssun1 |
|
112 |
111
|
a1i |
|
113 |
28
|
ntrss |
|
114 |
23 110 112 113
|
syl3anc |
|
115 |
114 31
|
sseldd |
|
116 |
115 49
|
elind |
|
117 |
42
|
a1i |
|
118 |
|
eqid |
|
119 |
28 118
|
restntr |
|
120 |
23 27 117 119
|
syl3anc |
|
121 |
|
restabs |
|
122 |
75 4 78 121
|
syl3anc |
|
123 |
122
|
fveq2d |
|
124 |
123
|
fveq1d |
|
125 |
120 124
|
eqtr3d |
|
126 |
116 125
|
eleqtrd |
|
127 |
|
undif1 |
|
128 |
49
|
snssd |
|
129 |
|
ssequn2 |
|
130 |
128 129
|
sylib |
|
131 |
127 130
|
eqtrid |
|
132 |
131
|
oveq2d |
|
133 |
132
|
fveq2d |
|
134 |
133 97
|
fveq12d |
|
135 |
126 134
|
eleqtrrd |
|
136 |
106 44 107 8 108 135
|
limcres |
|
137 |
44
|
resmptd |
|
138 |
137
|
oveq1d |
|
139 |
136 138
|
eqtr3d |
|
140 |
105 139
|
eleqtrd |
|
141 |
8
|
addcn |
|
142 |
5 1 2
|
dvcl |
|
143 |
6 142
|
mpdan |
|
144 |
5 3 4
|
dvcl |
|
145 |
7 144
|
mpdan |
|
146 |
143 145
|
opelxpd |
|
147 |
54
|
toponunii |
|
148 |
147
|
cncnpi |
|
149 |
141 146 148
|
sylancr |
|
150 |
41 51 52 52 8 55 104 140 149
|
limccnp2 |
|
151 |
|
eldifi |
|
152 |
151
|
adantl |
|
153 |
1
|
ffnd |
|
154 |
153
|
adantr |
|
155 |
3
|
ffnd |
|
156 |
155
|
adantr |
|
157 |
|
ssexg |
|
158 |
36 76 157
|
sylancl |
|
159 |
158
|
adantr |
|
160 |
|
ssexg |
|
161 |
46 76 160
|
sylancl |
|
162 |
161
|
adantr |
|
163 |
|
eqid |
|
164 |
|
eqidd |
|
165 |
|
eqidd |
|
166 |
154 156 159 162 163 164 165
|
ofval |
|
167 |
152 166
|
mpdan |
|
168 |
|
eqidd |
|
169 |
|
eqidd |
|
170 |
154 156 159 162 163 168 169
|
ofval |
|
171 |
93 170
|
mpidan |
|
172 |
167 171
|
oveq12d |
|
173 |
|
difss |
|
174 |
173 32
|
sstri |
|
175 |
174
|
sseli |
|
176 |
|
ffvelcdm |
|
177 |
1 175 176
|
syl2an |
|
178 |
173 42
|
sstri |
|
179 |
178
|
sseli |
|
180 |
|
ffvelcdm |
|
181 |
3 179 180
|
syl2an |
|
182 |
1 39
|
ffvelcdmd |
|
183 |
182
|
adantr |
|
184 |
3 49
|
ffvelcdmd |
|
185 |
184
|
adantr |
|
186 |
177 181 183 185
|
addsub4d |
|
187 |
172 186
|
eqtrd |
|
188 |
187
|
oveq1d |
|
189 |
177 183
|
subcld |
|
190 |
181 185
|
subcld |
|
191 |
174 36
|
sstrid |
|
192 |
191
|
sselda |
|
193 |
36 39
|
sseldd |
|
194 |
193
|
adantr |
|
195 |
192 194
|
subcld |
|
196 |
|
eldifsni |
|
197 |
196
|
adantl |
|
198 |
192 194 197
|
subne0d |
|
199 |
189 190 195 198
|
divdird |
|
200 |
188 199
|
eqtrd |
|
201 |
200
|
mpteq2dva |
|
202 |
201
|
oveq1d |
|
203 |
150 202
|
eleqtrrd |
|
204 |
|
eqid |
|
205 |
|
addcl |
|
206 |
205
|
adantl |
|
207 |
206 1 3 158 161 163
|
off |
|
208 |
9 8 204 5 207 60
|
eldv |
|
209 |
31 203 208
|
mpbir2and |
|