Step |
Hyp |
Ref |
Expression |
1 |
|
0cn |
|
2 |
|
ax-icn |
|
3 |
1 2
|
mulcli |
|
4 |
|
cnre |
|
5 |
|
simplr |
|
6 |
|
neqne |
|
7 |
6
|
adantl |
|
8 |
|
simplll |
|
9 |
|
rernegcl |
|
10 |
8 9
|
syl |
|
11 |
|
1red |
|
12 |
10 11
|
readdcld |
|
13 |
|
ax-rrecex |
|
14 |
12 13
|
sylan |
|
15 |
2
|
a1i |
|
16 |
10
|
recnd |
|
17 |
|
1cnd |
|
18 |
15 16 17
|
adddid |
|
19 |
|
it1ei |
|
20 |
19
|
oveq2i |
|
21 |
18 20
|
eqtrdi |
|
22 |
21
|
oveq2d |
|
23 |
|
0cnd |
|
24 |
15 16
|
mulcld |
|
25 |
23 24 15
|
adddid |
|
26 |
22 25
|
eqtrd |
|
27 |
5
|
oveq2d |
|
28 |
|
renegid2 |
|
29 |
28
|
ad3antrrr |
|
30 |
29
|
oveq1d |
|
31 |
8
|
recnd |
|
32 |
|
simpllr |
|
33 |
32
|
recnd |
|
34 |
15 33
|
mulcld |
|
35 |
16 31 34
|
addassd |
|
36 |
|
sn-addid2 |
|
37 |
34 36
|
syl |
|
38 |
30 35 37
|
3eqtr3d |
|
39 |
27 38
|
eqtrd |
|
40 |
39
|
oveq2d |
|
41 |
3
|
a1i |
|
42 |
41 16 41
|
adddid |
|
43 |
23 15 16
|
mulassd |
|
44 |
41 23 15
|
mulassd |
|
45 |
|
sn-mul01 |
|
46 |
41 45
|
syl |
|
47 |
46
|
oveq1d |
|
48 |
44 47
|
eqtr3d |
|
49 |
43 48
|
oveq12d |
|
50 |
42 49
|
eqtrd |
|
51 |
23 15 34
|
mulassd |
|
52 |
15 15 33
|
mulassd |
|
53 |
|
reixi |
|
54 |
|
1re |
|
55 |
|
rernegcl |
|
56 |
54 55
|
ax-mp |
|
57 |
53 56
|
eqeltri |
|
58 |
57
|
a1i |
|
59 |
58 32
|
remulcld |
|
60 |
52 59
|
eqeltrrd |
|
61 |
|
remul02 |
|
62 |
60 61
|
syl |
|
63 |
51 62
|
eqtrd |
|
64 |
40 50 63
|
3eqtr3d |
|
65 |
26 64
|
eqtrd |
|
66 |
65
|
ad2antrr |
|
67 |
66
|
oveq1d |
|
68 |
|
0cnd |
|
69 |
2
|
a1i |
|
70 |
10
|
ad2antrr |
|
71 |
70
|
recnd |
|
72 |
|
1cnd |
|
73 |
71 72
|
addcld |
|
74 |
69 73
|
mulcld |
|
75 |
|
simprl |
|
76 |
75
|
recnd |
|
77 |
68 74 76
|
mulassd |
|
78 |
69 73 76
|
mulassd |
|
79 |
|
simprr |
|
80 |
79
|
oveq2d |
|
81 |
80 19
|
eqtrdi |
|
82 |
78 81
|
eqtrd |
|
83 |
82
|
oveq2d |
|
84 |
77 83
|
eqtrd |
|
85 |
|
remul02 |
|
86 |
75 85
|
syl |
|
87 |
67 84 86
|
3eqtr3d |
|
88 |
14 87
|
rexlimddv |
|
89 |
88
|
ex |
|
90 |
89
|
necon1d |
|
91 |
7 90
|
mpd |
|
92 |
91
|
oveq2d |
|
93 |
31 16 17
|
addassd |
|
94 |
|
renegid |
|
95 |
8 94
|
syl |
|
96 |
95
|
oveq1d |
|
97 |
|
readdid2 |
|
98 |
54 97
|
ax-mp |
|
99 |
96 98
|
eqtrdi |
|
100 |
93 99
|
eqtr3d |
|
101 |
|
readdid1 |
|
102 |
8 101
|
syl |
|
103 |
92 100 102
|
3eqtr3rd |
|
104 |
|
rernegcl |
|
105 |
32 104
|
syl |
|
106 |
11 105
|
readdcld |
|
107 |
|
ax-rrecex |
|
108 |
106 107
|
sylan |
|
109 |
105
|
recnd |
|
110 |
15 109
|
mulcld |
|
111 |
23 15 110
|
adddid |
|
112 |
|
0re |
|
113 |
|
remul02 |
|
114 |
112 113
|
ax-mp |
|
115 |
114
|
oveq1i |
|
116 |
1 1 2
|
mulassi |
|
117 |
115 116
|
eqtr3i |
|
118 |
117
|
a1i |
|
119 |
118
|
oveq1d |
|
120 |
111 119
|
eqtrd |
|
121 |
15 17 109
|
adddid |
|
122 |
19
|
a1i |
|
123 |
122
|
oveq1d |
|
124 |
121 123
|
eqtrd |
|
125 |
124
|
oveq2d |
|
126 |
23 41 110
|
adddid |
|
127 |
120 125 126
|
3eqtr4d |
|
128 |
103
|
oveq1d |
|
129 |
5 128
|
eqtrd |
|
130 |
129
|
oveq1d |
|
131 |
17 34 110
|
addassd |
|
132 |
|
renegid |
|
133 |
32 132
|
syl |
|
134 |
133
|
oveq2d |
|
135 |
15 33 109
|
adddid |
|
136 |
|
sn-mul01 |
|
137 |
2 136
|
mp1i |
|
138 |
134 135 137
|
3eqtr3d |
|
139 |
138
|
oveq2d |
|
140 |
|
readdid1 |
|
141 |
54 140
|
ax-mp |
|
142 |
139 141
|
eqtrdi |
|
143 |
131 142
|
eqtrd |
|
144 |
130 143
|
eqtrd |
|
145 |
144
|
oveq2d |
|
146 |
127 145
|
eqtrd |
|
147 |
|
ax-1rid |
|
148 |
112 147
|
ax-mp |
|
149 |
146 148
|
eqtrdi |
|
150 |
149
|
ad2antrr |
|
151 |
150
|
oveq1d |
|
152 |
|
0cnd |
|
153 |
2
|
a1i |
|
154 |
|
1cnd |
|
155 |
109
|
ad2antrr |
|
156 |
154 155
|
addcld |
|
157 |
153 156
|
mulcld |
|
158 |
|
simprl |
|
159 |
158
|
recnd |
|
160 |
152 157 159
|
mulassd |
|
161 |
153 156 159
|
mulassd |
|
162 |
|
simprr |
|
163 |
162
|
oveq2d |
|
164 |
163 19
|
eqtrdi |
|
165 |
161 164
|
eqtrd |
|
166 |
165
|
oveq2d |
|
167 |
160 166
|
eqtrd |
|
168 |
|
remul02 |
|
169 |
158 168
|
syl |
|
170 |
151 167 169
|
3eqtr3d |
|
171 |
108 170
|
rexlimddv |
|
172 |
171
|
ex |
|
173 |
172
|
necon1d |
|
174 |
7 173
|
mpd |
|
175 |
174
|
oveq1d |
|
176 |
17 109 33
|
addassd |
|
177 |
|
renegid2 |
|
178 |
32 177
|
syl |
|
179 |
178
|
oveq2d |
|
180 |
179 141
|
eqtrdi |
|
181 |
176 180
|
eqtrd |
|
182 |
|
readdid2 |
|
183 |
32 182
|
syl |
|
184 |
175 181 183
|
3eqtr3rd |
|
185 |
184
|
oveq2d |
|
186 |
103 185
|
oveq12d |
|
187 |
5 186
|
eqtrd |
|
188 |
19
|
oveq2i |
|
189 |
188
|
eqeq2i |
|
190 |
|
oveq2 |
|
191 |
2 2
|
mulcli |
|
192 |
191 2
|
mulcli |
|
193 |
192 1 2
|
mulassi |
|
194 |
|
sn-mul01 |
|
195 |
192 194
|
ax-mp |
|
196 |
195
|
oveq1i |
|
197 |
193 196
|
eqtr3i |
|
198 |
|
ax-1cn |
|
199 |
192 198 2
|
adddii |
|
200 |
191 2 198
|
mulassi |
|
201 |
19
|
oveq2i |
|
202 |
200 201
|
eqtri |
|
203 |
191 2 2
|
mulassi |
|
204 |
|
rei4 |
|
205 |
203 204
|
eqtri |
|
206 |
202 205
|
oveq12i |
|
207 |
199 206
|
eqtri |
|
208 |
190 197 207
|
3eqtr3g |
|
209 |
54 54
|
readdcli |
|
210 |
|
df-2 |
|
211 |
|
sn-0ne2 |
|
212 |
211
|
necomi |
|
213 |
210 212
|
eqnetrri |
|
214 |
|
ax-rrecex |
|
215 |
209 213 214
|
mp2an |
|
216 |
192 198
|
addcli |
|
217 |
198 2 216
|
addassi |
|
218 |
2 192 198
|
addassi |
|
219 |
218
|
oveq2i |
|
220 |
2 2 2
|
mulassi |
|
221 |
220
|
oveq2i |
|
222 |
|
ipiiie0 |
|
223 |
221 222
|
eqtri |
|
224 |
223
|
oveq1i |
|
225 |
224 98
|
eqtri |
|
226 |
225
|
oveq2i |
|
227 |
217 219 226
|
3eqtr2i |
|
228 |
227
|
a1i |
|
229 |
3 198 198
|
adddii |
|
230 |
1 2 198
|
mulassi |
|
231 |
19
|
oveq2i |
|
232 |
230 231
|
eqtri |
|
233 |
|
simpl |
|
234 |
232 233
|
syl5eq |
|
235 |
|
simpr |
|
236 |
232 235
|
syl5eq |
|
237 |
234 236
|
oveq12d |
|
238 |
229 237
|
syl5eq |
|
239 |
|
remulid2 |
|
240 |
209 239
|
mp1i |
|
241 |
228 238 240
|
3eqtr4d |
|
242 |
241
|
oveq1d |
|
243 |
242
|
adantr |
|
244 |
3
|
a1i |
|
245 |
|
1cnd |
|
246 |
245 245
|
addcld |
|
247 |
|
simprl |
|
248 |
247
|
recnd |
|
249 |
244 246 248
|
mulassd |
|
250 |
|
simprr |
|
251 |
250
|
oveq2d |
|
252 |
251 232
|
eqtrdi |
|
253 |
249 252
|
eqtrd |
|
254 |
245 246 248
|
mulassd |
|
255 |
250
|
oveq2d |
|
256 |
|
1t1e1ALT |
|
257 |
255 256
|
eqtrdi |
|
258 |
254 257
|
eqtrd |
|
259 |
243 253 258
|
3eqtr3d |
|
260 |
259
|
rexlimdvaa |
|
261 |
215 260
|
mpi |
|
262 |
208 261
|
mpdan |
|
263 |
189 262
|
sylbi |
|
264 |
|
oveq2 |
|
265 |
116 115
|
eqtr3i |
|
266 |
264 265 148
|
3eqtr3g |
|
267 |
263 266
|
syl |
|
268 |
187 267
|
syl |
|
269 |
268
|
pm2.18da |
|
270 |
269
|
ex |
|
271 |
270
|
rexlimivv |
|
272 |
3 4 271
|
mp2b |
|