Step |
Hyp |
Ref |
Expression |
1 |
|
cubic2.a |
|
2 |
|
cubic2.z |
|
3 |
|
cubic2.b |
|
4 |
|
cubic2.c |
|
5 |
|
cubic2.d |
|
6 |
|
cubic2.x |
|
7 |
|
cubic2.t |
|
8 |
|
cubic2.3 |
|
9 |
|
cubic2.g |
|
10 |
|
cubic2.2 |
|
11 |
|
cubic2.m |
|
12 |
|
cubic2.n |
|
13 |
|
cubic2.0 |
|
14 |
|
3nn0 |
|
15 |
|
expcl |
|
16 |
6 14 15
|
sylancl |
|
17 |
1 16
|
mulcld |
|
18 |
6
|
sqcld |
|
19 |
3 18
|
mulcld |
|
20 |
17 19
|
addcld |
|
21 |
4 6
|
mulcld |
|
22 |
21 5
|
addcld |
|
23 |
20 22
|
addcld |
|
24 |
23 1 2
|
diveq0ad |
|
25 |
20 22 1 2
|
divdird |
|
26 |
17 19 1 2
|
divdird |
|
27 |
16 1 2
|
divcan3d |
|
28 |
3 18 1 2
|
div23d |
|
29 |
27 28
|
oveq12d |
|
30 |
26 29
|
eqtrd |
|
31 |
21 5 1 2
|
divdird |
|
32 |
4 6 1 2
|
div23d |
|
33 |
32
|
oveq1d |
|
34 |
31 33
|
eqtrd |
|
35 |
30 34
|
oveq12d |
|
36 |
25 35
|
eqtrd |
|
37 |
36
|
eqeq1d |
|
38 |
24 37
|
bitr3d |
|
39 |
3 1 2
|
divcld |
|
40 |
4 1 2
|
divcld |
|
41 |
5 1 2
|
divcld |
|
42 |
7 1 2
|
divcld |
|
43 |
14
|
a1i |
|
44 |
7 1 2 43
|
expdivd |
|
45 |
8
|
oveq1d |
|
46 |
|
2cn |
|
47 |
|
expcl |
|
48 |
3 14 47
|
sylancl |
|
49 |
|
mulcl |
|
50 |
46 48 49
|
sylancr |
|
51 |
|
9cn |
|
52 |
|
mulcl |
|
53 |
51 1 52
|
sylancr |
|
54 |
3 4
|
mulcld |
|
55 |
53 54
|
mulcld |
|
56 |
50 55
|
subcld |
|
57 |
|
2nn0 |
|
58 |
|
7nn |
|
59 |
57 58
|
decnncl |
|
60 |
59
|
nncni |
|
61 |
1
|
sqcld |
|
62 |
61 5
|
mulcld |
|
63 |
|
mulcl |
|
64 |
60 62 63
|
sylancr |
|
65 |
56 64
|
addcld |
|
66 |
12 65
|
eqeltrd |
|
67 |
66 9
|
addcld |
|
68 |
|
2cnd |
|
69 |
|
expcl |
|
70 |
1 14 69
|
sylancl |
|
71 |
|
2ne0 |
|
72 |
71
|
a1i |
|
73 |
|
3z |
|
74 |
73
|
a1i |
|
75 |
1 2 74
|
expne0d |
|
76 |
67 68 70 72 75
|
divdiv32d |
|
77 |
66 9 70 75
|
divdird |
|
78 |
77
|
oveq1d |
|
79 |
76 78
|
eqtrd |
|
80 |
44 45 79
|
3eqtrd |
|
81 |
9 70 75
|
divcld |
|
82 |
9 70 75
|
sqdivd |
|
83 |
10
|
oveq1d |
|
84 |
66
|
sqcld |
|
85 |
|
4cn |
|
86 |
3
|
sqcld |
|
87 |
|
3cn |
|
88 |
1 4
|
mulcld |
|
89 |
|
mulcl |
|
90 |
87 88 89
|
sylancr |
|
91 |
86 90
|
subcld |
|
92 |
11 91
|
eqeltrd |
|
93 |
|
expcl |
|
94 |
92 14 93
|
sylancl |
|
95 |
|
mulcl |
|
96 |
85 94 95
|
sylancr |
|
97 |
70
|
sqcld |
|
98 |
|
sqne0 |
|
99 |
70 98
|
syl |
|
100 |
75 99
|
mpbird |
|
101 |
84 96 97 100
|
divsubdird |
|
102 |
66 70 75
|
sqdivd |
|
103 |
|
2z |
|
104 |
103
|
a1i |
|
105 |
1 2 104
|
expne0d |
|
106 |
92 61 105 43
|
expdivd |
|
107 |
46 87
|
mulcomi |
|
108 |
107
|
oveq2i |
|
109 |
57
|
a1i |
|
110 |
1 43 109
|
expmuld |
|
111 |
1 109 43
|
expmuld |
|
112 |
108 110 111
|
3eqtr3a |
|
113 |
112
|
oveq2d |
|
114 |
106 113
|
eqtrd |
|
115 |
114
|
oveq2d |
|
116 |
85
|
a1i |
|
117 |
116 94 97 100
|
divassd |
|
118 |
115 117
|
eqtr4d |
|
119 |
102 118
|
oveq12d |
|
120 |
101 119
|
eqtr4d |
|
121 |
82 83 120
|
3eqtrd |
|
122 |
86 90 61 105
|
divsubdird |
|
123 |
11
|
oveq1d |
|
124 |
3 1 2
|
sqdivd |
|
125 |
1
|
sqvald |
|
126 |
125
|
oveq2d |
|
127 |
4 1 1 2 2
|
divcan5d |
|
128 |
126 127
|
eqtr2d |
|
129 |
128
|
oveq2d |
|
130 |
87
|
a1i |
|
131 |
130 88 61 105
|
divassd |
|
132 |
129 131
|
eqtr4d |
|
133 |
124 132
|
oveq12d |
|
134 |
122 123 133
|
3eqtr4d |
|
135 |
56 64 70 75
|
divdird |
|
136 |
12
|
oveq1d |
|
137 |
3 1 2 43
|
expdivd |
|
138 |
137
|
oveq2d |
|
139 |
68 48 70 75
|
divassd |
|
140 |
138 139
|
eqtr4d |
|
141 |
51
|
a1i |
|
142 |
1 54
|
mulcld |
|
143 |
141 142 70 75
|
divassd |
|
144 |
141 1 54
|
mulassd |
|
145 |
144
|
oveq1d |
|
146 |
54 61 1 105 2
|
divcan5d |
|
147 |
|
df-3 |
|
148 |
147
|
oveq2i |
|
149 |
|
expp1 |
|
150 |
1 57 149
|
sylancl |
|
151 |
148 150
|
syl5eq |
|
152 |
61 1
|
mulcomd |
|
153 |
151 152
|
eqtrd |
|
154 |
153
|
oveq2d |
|
155 |
3 1 4 1 2 2
|
divmuldivd |
|
156 |
125
|
oveq2d |
|
157 |
155 156
|
eqtr4d |
|
158 |
146 154 157
|
3eqtr4rd |
|
159 |
158
|
oveq2d |
|
160 |
143 145 159
|
3eqtr4rd |
|
161 |
140 160
|
oveq12d |
|
162 |
50 55 70 75
|
divsubdird |
|
163 |
161 162
|
eqtr4d |
|
164 |
151
|
oveq2d |
|
165 |
5 1 61 2 105
|
divcan5d |
|
166 |
164 165
|
eqtr2d |
|
167 |
166
|
oveq2d |
|
168 |
60
|
a1i |
|
169 |
168 62 70 75
|
divassd |
|
170 |
167 169
|
eqtr4d |
|
171 |
163 170
|
oveq12d |
|
172 |
135 136 171
|
3eqtr4d |
|
173 |
7 1 13 2
|
divne0d |
|
174 |
39 40 41 6 42 80 81 121 134 172 173
|
mcubic |
|
175 |
|
oveq1 |
|
176 |
|
3nn |
|
177 |
|
0exp |
|
178 |
176 177
|
ax-mp |
|
179 |
175 178
|
eqtrdi |
|
180 |
|
0ne1 |
|
181 |
180
|
a1i |
|
182 |
179 181
|
eqnetrd |
|
183 |
182
|
necon2i |
|
184 |
|
simprl |
|
185 |
7
|
adantr |
|
186 |
1
|
adantr |
|
187 |
2
|
adantr |
|
188 |
184 185 186 187
|
divassd |
|
189 |
188
|
eqcomd |
|
190 |
189
|
oveq2d |
|
191 |
3
|
adantr |
|
192 |
184 185
|
mulcld |
|
193 |
191 192 186 187
|
divdird |
|
194 |
190 193
|
eqtr4d |
|
195 |
92
|
adantr |
|
196 |
195 186 187
|
divcld |
|
197 |
|
simprr |
|
198 |
13
|
adantr |
|
199 |
184 185 197 198
|
mulne0d |
|
200 |
196 192 186 199 187
|
divcan7d |
|
201 |
195 186 186 187 187
|
divdiv1d |
|
202 |
186
|
sqvald |
|
203 |
202
|
oveq2d |
|
204 |
201 203
|
eqtr4d |
|
205 |
204 188
|
oveq12d |
|
206 |
195 186 192 187 199
|
divdiv32d |
|
207 |
200 205 206
|
3eqtr3d |
|
208 |
194 207
|
oveq12d |
|
209 |
191 192
|
addcld |
|
210 |
195 192 199
|
divcld |
|
211 |
209 210 186 187
|
divdird |
|
212 |
208 211
|
eqtr4d |
|
213 |
212
|
oveq1d |
|
214 |
209 210
|
addcld |
|
215 |
87
|
a1i |
|
216 |
|
3ne0 |
|
217 |
216
|
a1i |
|
218 |
214 186 215 187 217
|
divdiv1d |
|
219 |
|
mulcom |
|
220 |
186 87 219
|
sylancl |
|
221 |
220
|
oveq2d |
|
222 |
213 218 221
|
3eqtrd |
|
223 |
222
|
negeqd |
|
224 |
223
|
eqeq2d |
|
225 |
224
|
anassrs |
|
226 |
183 225
|
sylan2 |
|
227 |
226
|
pm5.32da |
|
228 |
227
|
rexbidva |
|
229 |
38 174 228
|
3bitrd |
|