Step |
Hyp |
Ref |
Expression |
1 |
|
ordtconn.x |
|
2 |
|
ordtconn.l |
|
3 |
|
ordtconn.j |
|
4 |
|
nfv |
|
5 |
|
nfcv |
|
6 |
|
nfra2w |
|
7 |
5 6
|
nfralw |
|
8 |
7
|
nfn |
|
9 |
4 8
|
nfan |
|
10 |
|
tospos |
|
11 |
|
posprs |
|
12 |
|
fvex |
|
13 |
12
|
inex1 |
|
14 |
2 13
|
eqeltri |
|
15 |
|
eqid |
|
16 |
15
|
ordttopon |
|
17 |
14 16
|
ax-mp |
|
18 |
1 2
|
prsdm |
|
19 |
18
|
fveq2d |
|
20 |
17 19
|
eleqtrid |
|
21 |
3 20
|
eqeltrid |
|
22 |
10 11 21
|
3syl |
|
23 |
22
|
ad3antrrr |
|
24 |
23
|
adantlr |
|
25 |
|
simpllr |
|
26 |
25
|
adantlr |
|
27 |
|
simpll |
|
28 |
27 10 11
|
3syl |
|
29 |
|
snex |
|
30 |
1
|
fvexi |
|
31 |
30
|
mptex |
|
32 |
31
|
rnex |
|
33 |
30
|
mptex |
|
34 |
33
|
rnex |
|
35 |
32 34
|
unex |
|
36 |
29 35
|
unex |
|
37 |
|
ssfii |
|
38 |
36 37
|
ax-mp |
|
39 |
|
fvex |
|
40 |
|
bastg |
|
41 |
39 40
|
ax-mp |
|
42 |
38 41
|
sstri |
|
43 |
|
eqid |
|
44 |
|
eqid |
|
45 |
1 2 43 44
|
ordtprsval |
|
46 |
3 45
|
syl5eq |
|
47 |
42 46
|
sseqtrrid |
|
48 |
47
|
unssbd |
|
49 |
28 48
|
syl |
|
50 |
49
|
unssbd |
|
51 |
|
breq2 |
|
52 |
51
|
notbid |
|
53 |
52
|
cbvrabv |
|
54 |
|
breq1 |
|
55 |
54
|
notbid |
|
56 |
55
|
rabbidv |
|
57 |
56
|
rspceeqv |
|
58 |
53 57
|
mpan2 |
|
59 |
30
|
rabex |
|
60 |
|
eqid |
|
61 |
60
|
elrnmpt |
|
62 |
59 61
|
ax-mp |
|
63 |
58 62
|
sylibr |
|
64 |
63
|
adantl |
|
65 |
50 64
|
sseldd |
|
66 |
65
|
ad2antrr |
|
67 |
49
|
unssad |
|
68 |
|
breq1 |
|
69 |
68
|
notbid |
|
70 |
69
|
cbvrabv |
|
71 |
|
breq2 |
|
72 |
71
|
notbid |
|
73 |
72
|
rabbidv |
|
74 |
73
|
rspceeqv |
|
75 |
70 74
|
mpan2 |
|
76 |
30
|
rabex |
|
77 |
|
eqid |
|
78 |
77
|
elrnmpt |
|
79 |
76 78
|
ax-mp |
|
80 |
75 79
|
sylibr |
|
81 |
80
|
adantl |
|
82 |
67 81
|
sseldd |
|
83 |
82
|
ad2antrr |
|
84 |
|
simpll |
|
85 |
|
simpr |
|
86 |
84 85
|
jca |
|
87 |
|
simplrl |
|
88 |
|
ssel |
|
89 |
88
|
ancrd |
|
90 |
89
|
anim1d |
|
91 |
90
|
impl |
|
92 |
|
elin |
|
93 |
|
breq2 |
|
94 |
93
|
notbid |
|
95 |
94
|
elrab |
|
96 |
95
|
anbi1i |
|
97 |
|
an32 |
|
98 |
92 96 97
|
3bitri |
|
99 |
91 98
|
sylibr |
|
100 |
99
|
ne0d |
|
101 |
25 100
|
sylanl1 |
|
102 |
101
|
r19.29an |
|
103 |
86 87 102
|
syl2anc |
|
104 |
|
simplrr |
|
105 |
|
ssel |
|
106 |
105
|
ancrd |
|
107 |
106
|
anim1d |
|
108 |
107
|
impl |
|
109 |
|
elin |
|
110 |
69
|
elrab |
|
111 |
110
|
anbi1i |
|
112 |
|
an32 |
|
113 |
109 111 112
|
3bitri |
|
114 |
108 113
|
sylibr |
|
115 |
114
|
ne0d |
|
116 |
25 115
|
sylanl1 |
|
117 |
116
|
r19.29an |
|
118 |
86 104 117
|
syl2anc |
|
119 |
1 2
|
trleile |
|
120 |
|
oran |
|
121 |
119 120
|
sylib |
|
122 |
121
|
3expa |
|
123 |
122
|
nrexdv |
|
124 |
|
rabid |
|
125 |
|
rabid |
|
126 |
124 125
|
anbi12i |
|
127 |
|
elin |
|
128 |
|
anandi |
|
129 |
126 127 128
|
3bitr4i |
|
130 |
129
|
exbii |
|
131 |
|
nfrab1 |
|
132 |
|
nfrab1 |
|
133 |
131 132
|
nfin |
|
134 |
133
|
n0f |
|
135 |
|
df-rex |
|
136 |
130 134 135
|
3bitr4i |
|
137 |
136
|
necon1bbii |
|
138 |
123 137
|
sylib |
|
139 |
138
|
adantlr |
|
140 |
139
|
adantr |
|
141 |
140
|
ineq1d |
|
142 |
|
0in |
|
143 |
141 142
|
eqtrdi |
|
144 |
143
|
adantlr |
|
145 |
|
simplr |
|
146 |
|
simpr |
|
147 |
|
vex |
|
148 |
147
|
snss |
|
149 |
|
eldif |
|
150 |
147
|
snss |
|
151 |
149 150
|
bitr3i |
|
152 |
|
ssconb |
|
153 |
151 152
|
syl5bb |
|
154 |
148 153
|
sylanb |
|
155 |
154
|
adantl |
|
156 |
155
|
anass1rs |
|
157 |
156
|
adantr |
|
158 |
145 146 157
|
mpbi2and |
|
159 |
10
|
ad3antrrr |
|
160 |
|
nfv |
|
161 |
131 132
|
nfun |
|
162 |
|
nfcv |
|
163 |
|
ianor |
|
164 |
1 2
|
posrasymb |
|
165 |
|
equcom |
|
166 |
164 165
|
syl6bb |
|
167 |
166
|
necon3bbid |
|
168 |
163 167
|
bitr3id |
|
169 |
168
|
3expia |
|
170 |
169
|
pm5.32d |
|
171 |
124 125
|
orbi12i |
|
172 |
|
elun |
|
173 |
|
andi |
|
174 |
171 172 173
|
3bitr4ri |
|
175 |
|
eldifsn |
|
176 |
175
|
bicomi |
|
177 |
170 174 176
|
3bitr3g |
|
178 |
160 161 162 177
|
eqrd |
|
179 |
159 145 178
|
syl2anc |
|
180 |
158 179
|
sseqtrrd |
|
181 |
180
|
adantlr |
|
182 |
24 26 66 83 103 118 144 181
|
nconnsubb |
|
183 |
182
|
anasss |
|
184 |
183
|
adantllr |
|
185 |
|
rexanali |
|
186 |
185
|
rexbii |
|
187 |
|
rexcom |
|
188 |
|
rexnal |
|
189 |
186 187 188
|
3bitr3i |
|
190 |
189
|
rexbii |
|
191 |
|
rexcom |
|
192 |
|
rexnal |
|
193 |
190 191 192
|
3bitr3i |
|
194 |
|
r19.41v |
|
195 |
194
|
rexbii |
|
196 |
|
r19.41v |
|
197 |
|
reeanv |
|
198 |
197
|
anbi1i |
|
199 |
195 196 198
|
3bitri |
|
200 |
199
|
rexbii |
|
201 |
193 200
|
bitr3i |
|
202 |
27
|
ad2antrr |
|
203 |
25
|
sselda |
|
204 |
|
simpllr |
|
205 |
1 2
|
trleile |
|
206 |
202 203 204 205
|
syl3anc |
|
207 |
|
simpr |
|
208 |
|
simplr |
|
209 |
|
nelne2 |
|
210 |
207 208 209
|
syl2anc |
|
211 |
159
|
adantr |
|
212 |
1 2
|
posrasymb |
|
213 |
212
|
necon3bbid |
|
214 |
211 203 204 213
|
syl3anc |
|
215 |
210 214
|
mpbird |
|
216 |
206 215
|
jca |
|
217 |
|
pm5.17 |
|
218 |
216 217
|
sylib |
|
219 |
218
|
rexbidva |
|
220 |
27
|
ad2antrr |
|
221 |
|
simpllr |
|
222 |
25
|
sselda |
|
223 |
1 2
|
trleile |
|
224 |
220 221 222 223
|
syl3anc |
|
225 |
|
simpr |
|
226 |
|
simplr |
|
227 |
|
nelne2 |
|
228 |
225 226 227
|
syl2anc |
|
229 |
228
|
necomd |
|
230 |
159
|
adantr |
|
231 |
1 2
|
posrasymb |
|
232 |
231
|
necon3bbid |
|
233 |
230 221 222 232
|
syl3anc |
|
234 |
229 233
|
mpbird |
|
235 |
224 234
|
jca |
|
236 |
|
pm5.17 |
|
237 |
235 236
|
sylib |
|
238 |
237
|
rexbidva |
|
239 |
219 238
|
anbi12d |
|
240 |
239
|
ex |
|
241 |
240
|
pm5.32rd |
|
242 |
241
|
rexbidva |
|
243 |
201 242
|
syl5bb |
|
244 |
243
|
biimpa |
|
245 |
9 184 244
|
r19.29af |
|
246 |
245
|
ex |
|
247 |
246
|
con4d |
|