Step |
Hyp |
Ref |
Expression |
1 |
|
constr0.1 |
|
2 |
|
constrfin.1 |
|
3 |
|
fveq2 |
|
4 |
3
|
eleq1d |
|
5 |
|
fveq2 |
|
6 |
5
|
eleq1d |
|
7 |
|
fveq2 |
|
8 |
7
|
eleq1d |
|
9 |
|
fveq2 |
|
10 |
9
|
eleq1d |
|
11 |
1
|
constr0 |
|
12 |
|
prfi |
|
13 |
11 12
|
eqeltri |
|
14 |
|
nfv |
|
15 |
|
nfcv |
|
16 |
|
nfrab1 |
|
17 |
|
nnon |
|
18 |
17
|
adantr |
|
19 |
|
eqid |
|
20 |
1 18 19
|
constrsuc |
|
21 |
|
rabid |
|
22 |
20 21
|
bitr4di |
|
23 |
14 15 16 22
|
eqrd |
|
24 |
|
3unrab |
|
25 |
23 24
|
eqtr4di |
|
26 |
|
simpr |
|
27 |
26
|
adantr |
|
28 |
27
|
adantr |
|
29 |
28
|
adantr |
|
30 |
|
snfi |
|
31 |
30
|
a1i |
|
32 |
1 17
|
constrsscn |
|
33 |
32
|
ad9antr |
|
34 |
|
simp-8r |
|
35 |
|
simp-7r |
|
36 |
|
simp-6r |
|
37 |
|
simp-5r |
|
38 |
|
simpllr |
|
39 |
|
simplr |
|
40 |
|
simpr1 |
|
41 |
|
simpr2 |
|
42 |
|
simpr3 |
|
43 |
|
eqid |
|
44 |
33 34 35 36 37 38 39 40 41 42 43
|
constrrtll |
|
45 |
44
|
r19.29an |
|
46 |
45
|
r19.29an |
|
47 |
46
|
ex |
|
48 |
47
|
ralrimiva |
|
49 |
|
rabsssn |
|
50 |
48 49
|
sylibr |
|
51 |
31 50
|
ssfid |
|
52 |
29 51
|
rabrexfi |
|
53 |
28 52
|
rabrexfi |
|
54 |
27 53
|
rabrexfi |
|
55 |
26 54
|
rabrexfi |
|
56 |
29
|
adantr |
|
57 |
|
snfi |
|
58 |
57
|
a1i |
|
59 |
32
|
ad10antr |
|
60 |
|
simp-9r |
|
61 |
|
simp-8r |
|
62 |
|
simp-7r |
|
63 |
|
simp-6r |
|
64 |
|
simp-5r |
|
65 |
|
simplr |
|
66 |
|
simprl |
|
67 |
|
simprr |
|
68 |
|
simp-4r |
|
69 |
59 60 61 62 63 64 65 66 67 68
|
constrrtlc2 |
|
70 |
69
|
r19.29an |
|
71 |
70
|
ex |
|
72 |
71
|
ralrimiva |
|
73 |
|
rabsssn |
|
74 |
72 73
|
sylibr |
|
75 |
58 74
|
ssfid |
|
76 |
|
prfi |
|
77 |
76
|
a1i |
|
78 |
|
simpllr |
|
79 |
|
1cnd |
|
80 |
|
ax-1ne0 |
|
81 |
80
|
a1i |
|
82 |
32
|
ad10antr |
|
83 |
|
simp-9r |
|
84 |
82 83
|
sseldd |
|
85 |
84
|
cjcld |
|
86 |
|
simp-8r |
|
87 |
82 86
|
sseldd |
|
88 |
87
|
cjcld |
|
89 |
88 85
|
subcld |
|
90 |
87 84
|
subcld |
|
91 |
|
simp-4r |
|
92 |
91
|
necomd |
|
93 |
87 84 92
|
subne0d |
|
94 |
89 90 93
|
divcld |
|
95 |
84 94
|
mulcld |
|
96 |
85 95
|
subcld |
|
97 |
|
simp-7r |
|
98 |
82 97
|
sseldd |
|
99 |
98
|
cjcld |
|
100 |
96 99
|
subcld |
|
101 |
98 94
|
mulcld |
|
102 |
100 101
|
subcld |
|
103 |
|
simp-6r |
|
104 |
|
simp-5r |
|
105 |
|
simplr |
|
106 |
|
simprl |
|
107 |
|
simprr |
|
108 |
|
eqid |
|
109 |
|
eqid |
|
110 |
|
eqid |
|
111 |
82 83 86 97 103 104 105 106 107 108 109 110 91
|
constrrtlc1 |
|
112 |
111
|
simprd |
|
113 |
102 94 112
|
divcld |
|
114 |
98 100
|
mulcld |
|
115 |
82 103
|
sseldd |
|
116 |
82 104
|
sseldd |
|
117 |
115 116
|
subcld |
|
118 |
115
|
cjcld |
|
119 |
116
|
cjcld |
|
120 |
118 119
|
subcld |
|
121 |
117 120
|
mulcld |
|
122 |
114 121
|
addcld |
|
123 |
122
|
negcld |
|
124 |
123 94 112
|
divcld |
|
125 |
78
|
sqcld |
|
126 |
125
|
mullidd |
|
127 |
126
|
oveq1d |
|
128 |
111
|
simpld |
|
129 |
127 128
|
eqtrd |
|
130 |
78 79 81 113 124 129
|
quad3d |
|
131 |
130
|
r19.29an |
|
132 |
131
|
ex |
|
133 |
132
|
ralrimiva |
|
134 |
|
rabsspr |
|
135 |
133 134
|
sylibr |
|
136 |
77 135
|
ssfid |
|
137 |
|
exmidne |
|
138 |
137
|
a1i |
|
139 |
75 136 138
|
mpjaodan |
|
140 |
56 139
|
rabrexfi |
|
141 |
29 140
|
rabrexfi |
|
142 |
28 141
|
rabrexfi |
|
143 |
27 142
|
rabrexfi |
|
144 |
26 143
|
rabrexfi |
|
145 |
55 144
|
unfid |
|
146 |
29
|
adantr |
|
147 |
146
|
adantr |
|
148 |
|
prfi |
|
149 |
148
|
a1i |
|
150 |
|
simplr |
|
151 |
|
1cnd |
|
152 |
80
|
a1i |
|
153 |
32
|
ad9antr |
|
154 |
|
simp-4r |
|
155 |
153 154
|
sseldd |
|
156 |
|
simpllr |
|
157 |
153 156
|
sseldd |
|
158 |
155 157
|
subcld |
|
159 |
158
|
cjcld |
|
160 |
158 159
|
mulcld |
|
161 |
|
simp-5r |
|
162 |
153 161
|
sseldd |
|
163 |
162
|
cjcld |
|
164 |
|
simp-8r |
|
165 |
153 164
|
sseldd |
|
166 |
162 165
|
addcld |
|
167 |
163 166
|
mulcld |
|
168 |
160 167
|
subcld |
|
169 |
|
simp-7r |
|
170 |
153 169
|
sseldd |
|
171 |
|
simp-6r |
|
172 |
153 171
|
sseldd |
|
173 |
170 172
|
subcld |
|
174 |
173
|
cjcld |
|
175 |
173 174
|
mulcld |
|
176 |
165
|
cjcld |
|
177 |
176 166
|
mulcld |
|
178 |
175 177
|
subcld |
|
179 |
168 178
|
subcld |
|
180 |
163 176
|
subcld |
|
181 |
162 165
|
cjsubd |
|
182 |
162 165
|
subcld |
|
183 |
|
simpr1 |
|
184 |
183
|
necomd |
|
185 |
162 165 184
|
subne0d |
|
186 |
182 185
|
cjne0d |
|
187 |
181 186
|
eqnetrrd |
|
188 |
179 180 187
|
divcld |
|
189 |
162 165
|
mulcld |
|
190 |
176 189
|
mulcld |
|
191 |
175 162
|
mulcld |
|
192 |
190 191
|
subcld |
|
193 |
163 189
|
mulcld |
|
194 |
160 165
|
mulcld |
|
195 |
193 194
|
subcld |
|
196 |
192 195
|
subcld |
|
197 |
196 180 187
|
divcld |
|
198 |
197
|
negcld |
|
199 |
150
|
sqcld |
|
200 |
199
|
mullidd |
|
201 |
200
|
oveq1d |
|
202 |
|
simpr2 |
|
203 |
|
simpr3 |
|
204 |
|
eqid |
|
205 |
|
eqid |
|
206 |
|
eqid |
|
207 |
|
eqid |
|
208 |
153 164 169 171 161 154 156 150 183 202 203 204 205 206 207
|
constrrtcc |
|
209 |
201 208
|
eqtrd |
|
210 |
150 151 152 188 198 209
|
quad3d |
|
211 |
210
|
ex |
|
212 |
211
|
ralrimiva |
|
213 |
|
rabsspr |
|
214 |
212 213
|
sylibr |
|
215 |
149 214
|
ssfid |
|
216 |
147 215
|
rabrexfi |
|
217 |
146 216
|
rabrexfi |
|
218 |
29 217
|
rabrexfi |
|
219 |
28 218
|
rabrexfi |
|
220 |
27 219
|
rabrexfi |
|
221 |
26 220
|
rabrexfi |
|
222 |
145 221
|
unfid |
|
223 |
25 222
|
eqeltrd |
|
224 |
223
|
ex |
|
225 |
4 6 8 10 13 224
|
finds |
|
226 |
2 225
|
syl |
|