Step |
Hyp |
Ref |
Expression |
1 |
|
ptbas.1 |
|
2 |
|
ptbasfi.2 |
|
3 |
1
|
elpt |
|
4 |
|
df-3an |
|
5 |
|
simprr |
|
6 |
|
disjdif2 |
|
7 |
6
|
raleqdv |
|
8 |
7
|
biimpac |
|
9 |
|
ixpeq2 |
|
10 |
8 9
|
syl |
|
11 |
|
fveq2 |
|
12 |
11
|
unieqd |
|
13 |
12
|
cbvixpv |
|
14 |
2 13
|
eqtri |
|
15 |
10 14
|
eqtr4di |
|
16 |
5 15
|
sylan |
|
17 |
|
ssv |
|
18 |
|
iineq1 |
|
19 |
|
0iin |
|
20 |
18 19
|
eqtrdi |
|
21 |
17 20
|
sseqtrrid |
|
22 |
21
|
adantl |
|
23 |
|
df-ss |
|
24 |
22 23
|
sylib |
|
25 |
16 24
|
eqtr4d |
|
26 |
|
simplll |
|
27 |
|
inss1 |
|
28 |
|
simpr |
|
29 |
27 28
|
sseldi |
|
30 |
|
fveq2 |
|
31 |
|
fveq2 |
|
32 |
30 31
|
eleq12d |
|
33 |
|
simprr |
|
34 |
33
|
ad2antrr |
|
35 |
32 34 29
|
rspcdva |
|
36 |
14
|
ptpjpre1 |
|
37 |
26 29 35 36
|
syl12anc |
|
38 |
37
|
adantlr |
|
39 |
38
|
iineq2dv |
|
40 |
|
simpr |
|
41 |
|
cnvimass |
|
42 |
|
eqid |
|
43 |
42
|
dmmptss |
|
44 |
41 43
|
sstri |
|
45 |
44 14
|
sseqtri |
|
46 |
45
|
rgenw |
|
47 |
|
r19.2z |
|
48 |
40 46 47
|
sylancl |
|
49 |
|
iinss |
|
50 |
48 49
|
syl |
|
51 |
50 14
|
sseqtrrdi |
|
52 |
|
sseqin2 |
|
53 |
51 52
|
sylib |
|
54 |
33
|
ad2antrr |
|
55 |
|
ssralv |
|
56 |
27 55
|
ax-mp |
|
57 |
|
elssuni |
|
58 |
|
iffalse |
|
59 |
58
|
sseq2d |
|
60 |
57 59
|
syl5ibrcom |
|
61 |
|
ssid |
|
62 |
|
iftrue |
|
63 |
62 30
|
eqtr4d |
|
64 |
61 63
|
sseqtrrid |
|
65 |
60 64
|
pm2.61d2 |
|
66 |
65
|
ralrimivw |
|
67 |
|
ssiin |
|
68 |
66 67
|
sylibr |
|
69 |
68
|
adantl |
|
70 |
62
|
equcoms |
|
71 |
|
fveq2 |
|
72 |
70 71
|
eqtrd |
|
73 |
72
|
sseq1d |
|
74 |
73
|
rspcev |
|
75 |
61 74
|
mpan2 |
|
76 |
|
iinss |
|
77 |
75 76
|
syl |
|
78 |
77
|
adantr |
|
79 |
69 78
|
eqssd |
|
80 |
79
|
ralimiaa |
|
81 |
54 56 80
|
3syl |
|
82 |
|
eldifn |
|
83 |
82
|
ad2antlr |
|
84 |
|
inss2 |
|
85 |
|
simpr |
|
86 |
84 85
|
sseldi |
|
87 |
|
eleq1 |
|
88 |
86 87
|
syl5ibrcom |
|
89 |
83 88
|
mtod |
|
90 |
89 58
|
syl |
|
91 |
90
|
iineq2dv |
|
92 |
|
iinconst |
|
93 |
92
|
adantr |
|
94 |
91 93
|
eqtr2d |
|
95 |
|
eqeq1 |
|
96 |
94 95
|
syl5ibrcom |
|
97 |
96
|
ralimdva |
|
98 |
5 97
|
mpan9 |
|
99 |
|
inundif |
|
100 |
99
|
raleqi |
|
101 |
|
ralunb |
|
102 |
100 101
|
bitr3i |
|
103 |
81 98 102
|
sylanbrc |
|
104 |
|
ixpeq2 |
|
105 |
103 104
|
syl |
|
106 |
|
ixpiin |
|
107 |
106
|
adantl |
|
108 |
105 107
|
eqtrd |
|
109 |
39 53 108
|
3eqtr4rd |
|
110 |
25 109
|
pm2.61dane |
|
111 |
|
ixpexg |
|
112 |
|
fvex |
|
113 |
112
|
uniex |
|
114 |
113
|
a1i |
|
115 |
111 114
|
mprg |
|
116 |
2 115
|
eqeltri |
|
117 |
116
|
mptex |
|
118 |
117
|
cnvex |
|
119 |
118
|
imaex |
|
120 |
119
|
dfiin2 |
|
121 |
|
inteq |
|
122 |
120 121
|
syl5eq |
|
123 |
|
int0 |
|
124 |
122 123
|
eqtrdi |
|
125 |
124
|
ineq2d |
|
126 |
|
inv1 |
|
127 |
125 126
|
eqtrdi |
|
128 |
127
|
adantl |
|
129 |
|
snex |
|
130 |
1
|
ptbas |
|
131 |
1 2
|
ptpjpre2 |
|
132 |
131
|
ralrimivva |
|
133 |
|
eqid |
|
134 |
133
|
fmpox |
|
135 |
132 134
|
sylib |
|
136 |
135
|
frnd |
|
137 |
130 136
|
ssexd |
|
138 |
|
unexg |
|
139 |
129 137 138
|
sylancr |
|
140 |
|
ssfii |
|
141 |
139 140
|
syl |
|
142 |
141
|
ad2antrr |
|
143 |
|
ssun1 |
|
144 |
116
|
snss |
|
145 |
143 144
|
mpbir |
|
146 |
145
|
a1i |
|
147 |
142 146
|
sseldd |
|
148 |
147
|
adantr |
|
149 |
128 148
|
eqeltrd |
|
150 |
139
|
ad3antrrr |
|
151 |
|
nfv |
|
152 |
|
nfcv |
|
153 |
|
nfcv |
|
154 |
|
nfixp1 |
|
155 |
2 154
|
nfcxfr |
|
156 |
|
nfcv |
|
157 |
155 156
|
nfmpt |
|
158 |
157
|
nfcnv |
|
159 |
|
nfcv |
|
160 |
158 159
|
nfima |
|
161 |
152 153 160
|
nfmpo |
|
162 |
161
|
nfrn |
|
163 |
162
|
nfcri |
|
164 |
|
df-ov |
|
165 |
119
|
a1i |
|
166 |
|
fveq2 |
|
167 |
166
|
mpteq2dv |
|
168 |
167
|
cnveqd |
|
169 |
168
|
imaeq1d |
|
170 |
|
imaeq2 |
|
171 |
169 170
|
sylan9eq |
|
172 |
|
fveq2 |
|
173 |
171 172 133
|
ovmpox |
|
174 |
29 35 165 173
|
syl3anc |
|
175 |
164 174
|
syl5eqr |
|
176 |
135
|
ad3antrrr |
|
177 |
176
|
ffnd |
|
178 |
|
opeliunxp |
|
179 |
29 35 178
|
sylanbrc |
|
180 |
|
sneq |
|
181 |
|
fveq2 |
|
182 |
180 181
|
xpeq12d |
|
183 |
182
|
cbviunv |
|
184 |
179 183
|
eleqtrdi |
|
185 |
|
fnfvelrn |
|
186 |
177 184 185
|
syl2anc |
|
187 |
175 186
|
eqeltrrd |
|
188 |
|
eleq1 |
|
189 |
187 188
|
syl5ibrcom |
|
190 |
189
|
ex |
|
191 |
151 163 190
|
rexlimd |
|
192 |
191
|
abssdv |
|
193 |
|
ssun2 |
|
194 |
192 193
|
sstrdi |
|
195 |
194
|
adantr |
|
196 |
|
simpr |
|
197 |
|
simplrl |
|
198 |
|
ssfi |
|
199 |
197 84 198
|
sylancl |
|
200 |
|
abrexfi |
|
201 |
199 200
|
syl |
|
202 |
|
elfir |
|
203 |
150 195 196 201 202
|
syl13anc |
|
204 |
120 203
|
eqeltrid |
|
205 |
|
elssuni |
|
206 |
204 205
|
syl |
|
207 |
|
fiuni |
|
208 |
139 207
|
syl |
|
209 |
116
|
pwid |
|
210 |
209
|
a1i |
|
211 |
210
|
snssd |
|
212 |
1
|
ptuni2 |
|
213 |
2 212
|
syl5eq |
|
214 |
|
eqimss2 |
|
215 |
213 214
|
syl |
|
216 |
|
sspwuni |
|
217 |
215 216
|
sylibr |
|
218 |
136 217
|
sstrd |
|
219 |
211 218
|
unssd |
|
220 |
|
sspwuni |
|
221 |
219 220
|
sylib |
|
222 |
|
elssuni |
|
223 |
145 222
|
mp1i |
|
224 |
221 223
|
eqssd |
|
225 |
208 224
|
eqtr3d |
|
226 |
225
|
ad3antrrr |
|
227 |
206 226
|
sseqtrd |
|
228 |
227 52
|
sylib |
|
229 |
228 204
|
eqeltrd |
|
230 |
149 229
|
pm2.61dane |
|
231 |
110 230
|
eqeltrd |
|
232 |
231
|
rexlimdvaa |
|
233 |
232
|
impr |
|
234 |
4 233
|
sylan2b |
|
235 |
|
eleq1 |
|
236 |
234 235
|
syl5ibrcom |
|
237 |
236
|
expimpd |
|
238 |
237
|
exlimdv |
|
239 |
3 238
|
syl5bi |
|
240 |
239
|
ssrdv |
|
241 |
1
|
ptbasid |
|
242 |
2 241
|
eqeltrid |
|
243 |
242
|
snssd |
|
244 |
243 136
|
unssd |
|
245 |
|
fiss |
|
246 |
130 244 245
|
syl2anc |
|
247 |
1
|
ptbasin2 |
|
248 |
246 247
|
sseqtrd |
|
249 |
240 248
|
eqssd |
|