Step |
Hyp |
Ref |
Expression |
1 |
|
no3indslem.a |
|
2 |
|
no3indslem.b |
|
3 |
|
no3indslem.1 |
|
4 |
|
no3indslem.2 |
|
5 |
|
no3indslem.3 |
|
6 |
|
no3indslem.4 |
|
7 |
|
no3indslem.5 |
|
8 |
|
no3indslem.6 |
|
9 |
|
no3indslem.7 |
|
10 |
|
no3indslem.8 |
|
11 |
|
no3indslem.9 |
|
12 |
|
no3indslem.10 |
|
13 |
|
no3indslem.11 |
|
14 |
|
no3indslem.12 |
Could not format ( z = C -> ( ka <-> al ) ) : No typesetting found for |- ( z = C -> ( ka <-> al ) ) with typecode |- |
15 |
|
no3indslem.i |
|
16 |
1
|
lrrecfr |
|
17 |
16
|
a1i |
|
18 |
2 17 17 17
|
frxp3 |
|
19 |
18
|
mptru |
|
20 |
1
|
lrrecpo |
|
21 |
20
|
a1i |
|
22 |
2 21 21 21
|
poxp3 |
|
23 |
22
|
mptru |
|
24 |
1
|
lrrecse |
|
25 |
24
|
a1i |
|
26 |
2 25 25 25
|
sexp3 |
|
27 |
26
|
mptru |
|
28 |
|
elxpxp |
|
29 |
2
|
xpord3pred |
|
30 |
1
|
lrrecpred |
|
31 |
30
|
3ad2ant1 |
|
32 |
31
|
uneq1d |
|
33 |
1
|
lrrecpred |
|
34 |
33
|
3ad2ant2 |
|
35 |
34
|
uneq1d |
|
36 |
32 35
|
xpeq12d |
|
37 |
1
|
lrrecpred |
|
38 |
37
|
3ad2ant3 |
|
39 |
38
|
uneq1d |
|
40 |
36 39
|
xpeq12d |
|
41 |
40
|
difeq1d |
|
42 |
29 41
|
eqtrd |
|
43 |
42
|
raleqdv |
|
44 |
|
eldif |
|
45 |
44
|
imbi1i |
|
46 |
|
impexp |
|
47 |
45 46
|
bitri |
|
48 |
47
|
ralbii2 |
|
49 |
43 48
|
bitrdi |
|
50 |
|
eleq1 |
|
51 |
50
|
notbid |
|
52 |
|
df-ne |
|
53 |
|
vex |
|
54 |
|
vex |
|
55 |
|
vex |
|
56 |
53 54 55
|
otthne |
|
57 |
52 56
|
bitr3i |
|
58 |
|
opex |
|
59 |
58
|
elsn |
|
60 |
57 59
|
xchnxbir |
|
61 |
51 60
|
bitrdi |
|
62 |
61 5
|
imbi12d |
|
63 |
62
|
ralxp3 |
|
64 |
|
ssun1 |
|
65 |
|
ssralv |
|
66 |
64 65
|
ax-mp |
|
67 |
|
ssun1 |
|
68 |
|
ssralv |
|
69 |
67 68
|
ax-mp |
|
70 |
|
ssun1 |
|
71 |
|
ssralv |
|
72 |
70 71
|
ax-mp |
|
73 |
72
|
ralimi |
|
74 |
69 73
|
syl |
|
75 |
74
|
ralimi |
|
76 |
66 75
|
syl |
|
77 |
76
|
adantl |
|
78 |
|
nfv |
|
79 |
|
nfra1 |
|
80 |
78 79
|
nfan |
|
81 |
|
nfv |
|
82 |
|
nfra2w |
|
83 |
81 82
|
nfan |
|
84 |
|
nfv |
|
85 |
83 84
|
nfan |
|
86 |
|
nfv |
|
87 |
|
nfcv |
|
88 |
|
nfra2w |
|
89 |
87 88
|
nfralw |
|
90 |
86 89
|
nfan |
|
91 |
|
nfv |
|
92 |
90 91
|
nfan |
|
93 |
|
nfv |
|
94 |
92 93
|
nfan |
|
95 |
|
simpl1 |
|
96 |
|
leftirr |
|
97 |
95 96
|
syl |
|
98 |
|
rightirr |
|
99 |
95 98
|
syl |
|
100 |
|
ioran |
|
101 |
97 99 100
|
sylanbrc |
|
102 |
|
eleq1w |
|
103 |
|
elun |
|
104 |
102 103
|
bitrdi |
|
105 |
104
|
notbid |
|
106 |
101 105
|
syl5ibrcom |
|
107 |
106
|
necon2ad |
|
108 |
107
|
imp |
|
109 |
108
|
3mix1d |
|
110 |
109
|
adantr |
|
111 |
110
|
adantr |
|
112 |
|
pm2.27 |
|
113 |
111 112
|
syl |
|
114 |
94 113
|
ralimda |
|
115 |
85 114
|
ralimda |
|
116 |
80 115
|
ralimda |
|
117 |
77 116
|
mpd |
|
118 |
|
ssun2 |
|
119 |
|
ssralv |
|
120 |
118 119
|
ax-mp |
|
121 |
120
|
ralimi |
|
122 |
69 121
|
syl |
|
123 |
122
|
ralimi |
|
124 |
66 123
|
syl |
|
125 |
124
|
adantl |
|
126 |
|
vex |
|
127 |
|
biidd |
|
128 |
|
biidd |
|
129 |
|
neeq1 |
|
130 |
127 128 129
|
3orbi123d |
|
131 |
130 6
|
imbi12d |
|
132 |
126 131
|
ralsn |
|
133 |
132
|
2ralbii |
|
134 |
125 133
|
sylib |
|
135 |
108
|
3mix1d |
|
136 |
135
|
adantr |
|
137 |
|
pm2.27 |
|
138 |
136 137
|
syl |
|
139 |
85 138
|
ralimda |
|
140 |
80 139
|
ralimda |
|
141 |
134 140
|
mpd |
|
142 |
|
ssun2 |
|
143 |
|
ssralv |
|
144 |
142 143
|
ax-mp |
|
145 |
72
|
ralimi |
|
146 |
144 145
|
syl |
|
147 |
146
|
ralimi |
|
148 |
66 147
|
syl |
|
149 |
148
|
adantl |
|
150 |
|
vex |
|
151 |
|
biidd |
|
152 |
|
neeq1 |
|
153 |
|
biidd |
|
154 |
151 152 153
|
3orbi123d |
|
155 |
154 7
|
imbi12d |
|
156 |
155
|
ralbidv |
|
157 |
150 156
|
ralsn |
|
158 |
157
|
ralbii |
|
159 |
149 158
|
sylib |
|
160 |
108
|
3mix1d |
|
161 |
160
|
adantr |
|
162 |
|
pm2.27 |
|
163 |
161 162
|
syl |
|
164 |
92 163
|
ralimda |
|
165 |
80 164
|
ralimda |
|
166 |
159 165
|
mpd |
|
167 |
117 141 166
|
3jca |
|
168 |
120
|
ralimi |
|
169 |
144 168
|
syl |
|
170 |
169
|
ralimi |
|
171 |
66 170
|
syl |
|
172 |
171
|
adantl |
|
173 |
155
|
ralbidv |
|
174 |
150 173
|
ralsn |
|
175 |
|
biidd |
|
176 |
127 175 129
|
3orbi123d |
|
177 |
176 8
|
imbi12d |
|
178 |
126 177
|
ralsn |
|
179 |
174 178
|
bitri |
|
180 |
179
|
ralbii |
|
181 |
172 180
|
sylib |
|
182 |
108
|
3mix1d |
|
183 |
|
pm2.27 |
|
184 |
182 183
|
syl |
|
185 |
80 184
|
ralimda |
|
186 |
181 185
|
mpd |
|
187 |
|
ssun2 |
|
188 |
|
ssralv |
|
189 |
187 188
|
ax-mp |
|
190 |
74
|
ralimi |
|
191 |
189 190
|
syl |
|
192 |
191
|
adantl |
|
193 |
|
vex |
|
194 |
|
neeq1 |
|
195 |
|
biidd |
|
196 |
|
biidd |
|
197 |
194 195 196
|
3orbi123d |
|
198 |
197 9
|
imbi12d |
|
199 |
198
|
2ralbidv |
|
200 |
193 199
|
ralsn |
|
201 |
192 200
|
sylib |
|
202 |
90 93
|
nfan |
|
203 |
|
simpl2 |
|
204 |
|
leftirr |
|
205 |
203 204
|
syl |
|
206 |
|
rightirr |
|
207 |
203 206
|
syl |
|
208 |
|
ioran |
|
209 |
205 207 208
|
sylanbrc |
|
210 |
|
eleq1w |
|
211 |
|
elun |
|
212 |
210 211
|
bitrdi |
|
213 |
212
|
notbid |
|
214 |
209 213
|
syl5ibrcom |
|
215 |
214
|
necon2ad |
|
216 |
215
|
imp |
|
217 |
216
|
adantr |
|
218 |
217
|
3mix2d |
|
219 |
|
pm2.27 |
|
220 |
218 219
|
syl |
|
221 |
202 220
|
ralimda |
|
222 |
83 221
|
ralimda |
|
223 |
201 222
|
mpd |
|
224 |
122
|
ralimi |
|
225 |
189 224
|
syl |
|
226 |
225
|
adantl |
|
227 |
198
|
2ralbidv |
|
228 |
193 227
|
ralsn |
|
229 |
|
biidd |
|
230 |
229 128 129
|
3orbi123d |
|
231 |
230 10
|
imbi12d |
|
232 |
126 231
|
ralsn |
|
233 |
232
|
ralbii |
|
234 |
228 233
|
bitri |
|
235 |
226 234
|
sylib |
|
236 |
216
|
3mix2d |
|
237 |
|
pm2.27 |
|
238 |
236 237
|
syl |
|
239 |
83 238
|
ralimda |
|
240 |
235 239
|
mpd |
|
241 |
186 223 240
|
3jca |
|
242 |
146
|
ralimi |
|
243 |
189 242
|
syl |
|
244 |
243
|
adantl |
|
245 |
198
|
2ralbidv |
|
246 |
193 245
|
ralsn |
|
247 |
|
biidd |
|
248 |
247 152 153
|
3orbi123d |
|
249 |
248 11
|
imbi12d |
|
250 |
249
|
ralbidv |
|
251 |
150 250
|
ralsn |
|
252 |
246 251
|
bitri |
|
253 |
244 252
|
sylib |
|
254 |
|
simpl3 |
|
255 |
|
leftirr |
|
256 |
254 255
|
syl |
|
257 |
|
rightirr |
|
258 |
254 257
|
syl |
|
259 |
|
ioran |
|
260 |
256 258 259
|
sylanbrc |
|
261 |
|
eleq1w |
|
262 |
|
elun |
|
263 |
261 262
|
bitrdi |
|
264 |
263
|
notbid |
|
265 |
260 264
|
syl5ibrcom |
|
266 |
265
|
necon2ad |
|
267 |
266
|
imp |
|
268 |
267
|
3mix3d |
|
269 |
|
pm2.27 |
|
270 |
268 269
|
syl |
|
271 |
90 270
|
ralimda |
|
272 |
253 271
|
mpd |
|
273 |
167 241 272
|
3jca |
|
274 |
273
|
ex |
|
275 |
274 15
|
syld |
|
276 |
63 275
|
syl5bi |
|
277 |
49 276
|
sylbid |
|
278 |
|
predeq3 |
|
279 |
278
|
raleqdv |
|
280 |
279 4
|
imbi12d |
|
281 |
277 280
|
syl5ibrcom |
|
282 |
281
|
3expa |
|
283 |
282
|
rexlimdva |
|
284 |
283
|
rexlimivv |
|
285 |
28 284
|
sylbi |
|
286 |
285 3
|
frpoins2g |
|
287 |
19 23 27 286
|
mp3an |
|
288 |
4
|
ralxp3 |
|
289 |
287 288
|
mpbi |
|
290 |
12 13 14
|
rspc3v |
Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( A. x e. No A. y e. No A. z e. No ch -> al ) ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( A. x e. No A. y e. No A. z e. No ch -> al ) ) with typecode |- |
291 |
289 290
|
mpi |
Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> al ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> al ) with typecode |- |