Step |
Hyp |
Ref |
Expression |
1 |
|
ubth.1 |
|
2 |
|
ubth.2 |
|
3 |
|
ubthlem.3 |
|
4 |
|
ubthlem.4 |
|
5 |
|
ubthlem.5 |
|
6 |
|
ubthlem.6 |
|
7 |
|
ubthlem.7 |
|
8 |
|
ubthlem.8 |
|
9 |
|
ubthlem.9 |
|
10 |
|
rzal |
|
11 |
10
|
ralrimivw |
|
12 |
|
rabid2 |
|
13 |
11 12
|
sylibr |
|
14 |
13
|
eqcomd |
|
15 |
14
|
eleq1d |
|
16 |
|
iinrab |
|
17 |
16
|
adantl |
|
18 |
|
id |
|
19 |
7
|
sselda |
|
20 |
|
eqid |
|
21 |
|
eqid |
|
22 |
|
eqid |
|
23 |
|
bnnv |
|
24 |
5 23
|
ax-mp |
|
25 |
3 20 4 21 22 24 6
|
blocn2 |
|
26 |
1 3
|
cbncms |
|
27 |
5 26
|
ax-mp |
|
28 |
|
cmetmet |
|
29 |
|
metxmet |
|
30 |
27 28 29
|
mp2b |
|
31 |
4
|
mopntopon |
|
32 |
30 31
|
ax-mp |
|
33 |
|
eqid |
|
34 |
33 20
|
imsxmet |
|
35 |
6 34
|
ax-mp |
|
36 |
21
|
mopntopon |
|
37 |
35 36
|
ax-mp |
|
38 |
|
iscncl |
|
39 |
32 37 38
|
mp2an |
|
40 |
25 39
|
sylib |
|
41 |
19 40
|
syl |
|
42 |
41
|
simpld |
|
43 |
42
|
adantlr |
|
44 |
43
|
ffvelrnda |
|
45 |
44
|
biantrurd |
|
46 |
|
fveq2 |
|
47 |
46
|
breq1d |
|
48 |
47
|
elrab |
|
49 |
45 48
|
bitr4di |
|
50 |
49
|
pm5.32da |
|
51 |
|
2fveq3 |
|
52 |
51
|
breq1d |
|
53 |
52
|
elrab |
|
54 |
53
|
a1i |
|
55 |
|
ffn |
|
56 |
|
elpreima |
|
57 |
43 55 56
|
3syl |
|
58 |
50 54 57
|
3bitr4d |
|
59 |
58
|
eqrdv |
|
60 |
|
imaeq2 |
|
61 |
60
|
eleq1d |
|
62 |
41
|
simprd |
|
63 |
62
|
adantlr |
|
64 |
|
nnre |
|
65 |
64
|
ad2antlr |
|
66 |
65
|
rexrd |
|
67 |
|
eqid |
|
68 |
33 67
|
nvzcl |
|
69 |
6 68
|
ax-mp |
|
70 |
33 67 2 20
|
nvnd |
|
71 |
6 70
|
mpan |
|
72 |
|
xmetsym |
|
73 |
35 69 72
|
mp3an12 |
|
74 |
71 73
|
eqtr4d |
|
75 |
74
|
breq1d |
|
76 |
75
|
rabbiia |
|
77 |
21 76
|
blcld |
|
78 |
35 69 77
|
mp3an12 |
|
79 |
66 78
|
syl |
|
80 |
61 63 79
|
rspcdva |
|
81 |
59 80
|
eqeltrd |
|
82 |
81
|
ralrimiva |
|
83 |
|
iincld |
|
84 |
18 82 83
|
syl2anr |
|
85 |
17 84
|
eqeltrrd |
|
86 |
4
|
mopntop |
|
87 |
30 86
|
ax-mp |
|
88 |
32
|
toponunii |
|
89 |
88
|
topcld |
|
90 |
87 89
|
ax-mp |
|
91 |
90
|
a1i |
|
92 |
15 85 91
|
pm2.61ne |
|
93 |
92 9
|
fmptd |
|
94 |
93
|
frnd |
|
95 |
88
|
cldss2 |
|
96 |
94 95
|
sstrdi |
|
97 |
|
sspwuni |
|
98 |
96 97
|
sylib |
|
99 |
|
arch |
|
100 |
99
|
adantl |
|
101 |
|
simpr |
|
102 |
|
ltle |
|
103 |
101 64 102
|
syl2an |
|
104 |
103
|
impr |
|
105 |
104
|
adantr |
|
106 |
42
|
ffvelrnda |
|
107 |
106
|
an32s |
|
108 |
33 2
|
nvcl |
|
109 |
6 107 108
|
sylancr |
|
110 |
109
|
adantlr |
|
111 |
110
|
adantlr |
|
112 |
|
simpllr |
|
113 |
|
simplrl |
|
114 |
113 64
|
syl |
|
115 |
|
letr |
|
116 |
111 112 114 115
|
syl3anc |
|
117 |
105 116
|
mpan2d |
|
118 |
117
|
ralimdva |
|
119 |
118
|
expr |
|
120 |
1
|
fvexi |
|
121 |
120
|
rabex |
|
122 |
9
|
fvmpt2 |
|
123 |
121 122
|
mpan2 |
|
124 |
123
|
eleq2d |
|
125 |
52
|
ralbidv |
|
126 |
125
|
elrab |
|
127 |
124 126
|
bitrdi |
|
128 |
|
simpr |
|
129 |
128
|
biantrurd |
|
130 |
129
|
bicomd |
|
131 |
127 130
|
sylan9bbr |
|
132 |
93
|
ffnd |
|
133 |
132
|
adantr |
|
134 |
|
fnfvelrn |
|
135 |
|
elssuni |
|
136 |
134 135
|
syl |
|
137 |
136
|
sseld |
|
138 |
133 137
|
sylan |
|
139 |
131 138
|
sylbird |
|
140 |
139
|
adantlr |
|
141 |
119 140
|
syl6d |
|
142 |
141
|
rexlimdva |
|
143 |
100 142
|
mpd |
|
144 |
143
|
rexlimdva |
|
145 |
144
|
ralimdva |
|
146 |
8 145
|
mpd |
|
147 |
|
dfss3 |
|
148 |
146 147
|
sylibr |
|
149 |
98 148
|
eqssd |
|
150 |
|
eqid |
|
151 |
1 150
|
nvzcl |
|
152 |
|
ne0i |
|
153 |
24 151 152
|
mp2b |
|
154 |
4
|
bcth2 |
|
155 |
27 153 154
|
mpanl12 |
|
156 |
93 149 155
|
syl2anc |
|
157 |
|
ffvelrn |
|
158 |
95 157
|
sseldi |
|
159 |
158
|
elpwid |
|
160 |
93 159
|
sylan |
|
161 |
88
|
ntrss3 |
|
162 |
87 160 161
|
sylancr |
|
163 |
162
|
sseld |
|
164 |
88
|
ntropn |
|
165 |
87 160 164
|
sylancr |
|
166 |
4
|
mopni2 |
|
167 |
30 166
|
mp3an1 |
|
168 |
165 167
|
sylan |
|
169 |
|
elssuni |
|
170 |
169 88
|
sseqtrrdi |
|
171 |
165 170
|
syl |
|
172 |
171
|
sselda |
|
173 |
88
|
ntrss2 |
|
174 |
87 160 173
|
sylancr |
|
175 |
|
sstr2 |
|
176 |
174 175
|
syl5com |
|
177 |
176
|
ad2antrr |
|
178 |
|
simpr |
|
179 |
178 30
|
jctil |
|
180 |
|
rphalfcl |
|
181 |
180
|
rpxrd |
|
182 |
|
rpxr |
|
183 |
|
rphalflt |
|
184 |
181 182 183
|
3jca |
|
185 |
|
eqid |
|
186 |
4 185
|
blsscls2 |
|
187 |
179 184 186
|
syl2an |
|
188 |
|
sstr2 |
|
189 |
187 188
|
syl |
|
190 |
180
|
adantl |
|
191 |
|
breq2 |
|
192 |
191
|
rabbidv |
|
193 |
192
|
sseq1d |
|
194 |
193
|
rspcev |
|
195 |
194
|
ex |
|
196 |
190 195
|
syl |
|
197 |
177 189 196
|
3syld |
|
198 |
197
|
rexlimdva |
|
199 |
172 198
|
syldan |
|
200 |
168 199
|
mpd |
|
201 |
200
|
ex |
|
202 |
163 201
|
jcad |
|
203 |
202
|
eximdv |
|
204 |
|
n0 |
|
205 |
|
df-rex |
|
206 |
203 204 205
|
3imtr4g |
|
207 |
206
|
reximdva |
|
208 |
156 207
|
mpd |
|