Step |
Hyp |
Ref |
Expression |
1 |
|
atansopn.d |
|
2 |
|
atansopn.s |
|
3 |
|
cnelprrecn |
|
4 |
3
|
a1i |
|
5 |
|
ax-1cn |
|
6 |
|
ax-icn |
|
7 |
1 2
|
atansssdm |
|
8 |
|
simpr |
|
9 |
7 8
|
sseldi |
|
10 |
|
atandm2 |
|
11 |
9 10
|
sylib |
|
12 |
11
|
simp1d |
|
13 |
|
mulcl |
|
14 |
6 12 13
|
sylancr |
|
15 |
|
subcl |
|
16 |
5 14 15
|
sylancr |
|
17 |
11
|
simp2d |
|
18 |
16 17
|
logcld |
|
19 |
|
addcl |
|
20 |
5 14 19
|
sylancr |
|
21 |
11
|
simp3d |
|
22 |
20 21
|
logcld |
|
23 |
18 22
|
subcld |
|
24 |
|
ovexd |
|
25 |
|
ovexd |
|
26 |
1 2
|
atans2 |
|
27 |
26
|
simp2bi |
|
28 |
27
|
adantl |
|
29 |
|
negex |
|
30 |
29
|
a1i |
|
31 |
1
|
logdmss |
|
32 |
|
simpr |
|
33 |
31 32
|
sseldi |
|
34 |
|
logf1o |
|
35 |
|
f1of |
|
36 |
34 35
|
ax-mp |
|
37 |
36
|
ffvelrni |
|
38 |
|
logrncn |
|
39 |
33 37 38
|
3syl |
|
40 |
|
ovexd |
|
41 |
6
|
a1i |
|
42 |
41 13
|
sylan |
|
43 |
5 42 15
|
sylancr |
|
44 |
29
|
a1i |
|
45 |
|
1cnd |
|
46 |
|
0cnd |
|
47 |
|
1cnd |
|
48 |
4 47
|
dvmptc |
|
49 |
6
|
a1i |
|
50 |
|
simpr |
|
51 |
4
|
dvmptid |
|
52 |
4 50 45 51 41
|
dvmptcmul |
|
53 |
6
|
mulid1i |
|
54 |
53
|
mpteq2i |
|
55 |
52 54
|
eqtrdi |
|
56 |
4 45 46 48 42 49 55
|
dvmptsub |
|
57 |
|
df-neg |
|
58 |
57
|
mpteq2i |
|
59 |
56 58
|
eqtr4di |
|
60 |
2
|
ssrab3 |
|
61 |
60
|
a1i |
|
62 |
|
eqid |
|
63 |
62
|
cnfldtopon |
|
64 |
63
|
toponrestid |
|
65 |
1 2
|
atansopn |
|
66 |
65
|
a1i |
|
67 |
4 43 44 59 61 64 62 66
|
dvmptres |
|
68 |
|
fssres |
|
69 |
36 31 68
|
mp2an |
|
70 |
69
|
a1i |
|
71 |
70
|
feqmptd |
|
72 |
|
fvres |
|
73 |
72
|
mpteq2ia |
|
74 |
71 73
|
eqtr2di |
|
75 |
74
|
oveq2d |
|
76 |
1
|
dvlog |
|
77 |
75 76
|
eqtrdi |
|
78 |
|
fveq2 |
|
79 |
|
oveq2 |
|
80 |
4 4 28 30 39 40 67 77 78 79
|
dvmptco |
|
81 |
|
irec |
|
82 |
81
|
oveq2i |
|
83 |
6
|
a1i |
|
84 |
|
ine0 |
|
85 |
84
|
a1i |
|
86 |
16 83 17 85
|
recdiv2d |
|
87 |
16 17
|
reccld |
|
88 |
87 83 85
|
divrecd |
|
89 |
|
1cnd |
|
90 |
89 14 83
|
subdird |
|
91 |
6
|
mulid2i |
|
92 |
91
|
a1i |
|
93 |
83 12 83
|
mul32d |
|
94 |
|
ixi |
|
95 |
94
|
oveq1i |
|
96 |
12
|
mulm1d |
|
97 |
95 96
|
syl5eq |
|
98 |
93 97
|
eqtrd |
|
99 |
92 98
|
oveq12d |
|
100 |
|
subneg |
|
101 |
6 12 100
|
sylancr |
|
102 |
90 99 101
|
3eqtrd |
|
103 |
83 12 102
|
comraddd |
|
104 |
103
|
oveq2d |
|
105 |
86 88 104
|
3eqtr3d |
|
106 |
82 105
|
syl5eqr |
|
107 |
106
|
mpteq2dva |
|
108 |
80 107
|
eqtrd |
|
109 |
|
ovexd |
|
110 |
26
|
simp3bi |
|
111 |
110
|
adantl |
|
112 |
5 42 19
|
sylancr |
|
113 |
4 45 46 48 42 49 55
|
dvmptadd |
|
114 |
6
|
addid2i |
|
115 |
114
|
mpteq2i |
|
116 |
113 115
|
eqtrdi |
|
117 |
4 112 49 116 61 64 62 66
|
dvmptres |
|
118 |
|
fveq2 |
|
119 |
|
oveq2 |
|
120 |
4 4 111 83 39 40 117 77 118 119
|
dvmptco |
|
121 |
89 20 83 21 85
|
divdiv2d |
|
122 |
89 14 83 85
|
divdird |
|
123 |
81
|
a1i |
|
124 |
12 83 85
|
divcan3d |
|
125 |
123 124
|
oveq12d |
|
126 |
|
negicn |
|
127 |
|
addcom |
|
128 |
126 12 127
|
sylancr |
|
129 |
|
negsub |
|
130 |
12 6 129
|
sylancl |
|
131 |
128 130
|
eqtrd |
|
132 |
122 125 131
|
3eqtrd |
|
133 |
132
|
oveq2d |
|
134 |
89 83 20 21
|
div23d |
|
135 |
121 133 134
|
3eqtr3rd |
|
136 |
135
|
mpteq2dva |
|
137 |
120 136
|
eqtrd |
|
138 |
4 18 25 108 22 109 137
|
dvmptsub |
|
139 |
|
subcl |
|
140 |
12 6 139
|
sylancl |
|
141 |
|
addcl |
|
142 |
12 6 141
|
sylancl |
|
143 |
12
|
sqcld |
|
144 |
|
addcl |
|
145 |
5 143 144
|
sylancr |
|
146 |
|
atandm4 |
|
147 |
146
|
simprbi |
|
148 |
9 147
|
syl |
|
149 |
140 142 145 148
|
divsubdird |
|
150 |
130
|
oveq1d |
|
151 |
126
|
a1i |
|
152 |
12 151 83
|
pnpcand |
|
153 |
150 152
|
eqtr3d |
|
154 |
|
2cn |
|
155 |
154 6 84
|
divreci |
|
156 |
81
|
oveq2i |
|
157 |
155 156
|
eqtri |
|
158 |
126
|
2timesi |
|
159 |
126 6
|
negsubi |
|
160 |
157 158 159
|
3eqtri |
|
161 |
153 160
|
eqtr4di |
|
162 |
161
|
oveq1d |
|
163 |
140
|
mulid1d |
|
164 |
140 142
|
mulcomd |
|
165 |
|
i2 |
|
166 |
165
|
oveq2i |
|
167 |
|
subneg |
|
168 |
143 5 167
|
sylancl |
|
169 |
166 168
|
syl5eq |
|
170 |
|
subsq |
|
171 |
12 6 170
|
sylancl |
|
172 |
|
addcom |
|
173 |
143 5 172
|
sylancl |
|
174 |
169 171 173
|
3eqtr3d |
|
175 |
164 174
|
eqtrd |
|
176 |
163 175
|
oveq12d |
|
177 |
|
subneg |
|
178 |
12 6 177
|
sylancl |
|
179 |
|
atandm |
|
180 |
9 179
|
sylib |
|
181 |
180
|
simp2d |
|
182 |
|
subeq0 |
|
183 |
182
|
necon3bid |
|
184 |
12 126 183
|
sylancl |
|
185 |
181 184
|
mpbird |
|
186 |
178 185
|
eqnetrrd |
|
187 |
180
|
simp3d |
|
188 |
|
subeq0 |
|
189 |
188
|
necon3bid |
|
190 |
12 6 189
|
sylancl |
|
191 |
187 190
|
mpbird |
|
192 |
89 142 140 186 191
|
divcan5d |
|
193 |
176 192
|
eqtr3d |
|
194 |
142
|
mulid1d |
|
195 |
194 174
|
oveq12d |
|
196 |
89 140 142 191 186
|
divcan5d |
|
197 |
195 196
|
eqtr3d |
|
198 |
193 197
|
oveq12d |
|
199 |
149 162 198
|
3eqtr3rd |
|
200 |
199
|
mpteq2dva |
|
201 |
138 200
|
eqtrd |
|
202 |
|
halfcl |
|
203 |
6 202
|
mp1i |
|
204 |
4 23 24 201 203
|
dvmptcmul |
|
205 |
|
df-atan |
|
206 |
205
|
reseq1i |
|
207 |
|
atanf |
|
208 |
207
|
fdmi |
|
209 |
7 208
|
sseqtri |
|
210 |
|
resmpt |
|
211 |
209 210
|
ax-mp |
|
212 |
206 211
|
eqtri |
|
213 |
212
|
a1i |
|
214 |
213
|
oveq2d |
|
215 |
|
2ne0 |
|
216 |
|
divcan6 |
|
217 |
6 84 154 215 216
|
mp4an |
|
218 |
217
|
oveq1i |
|
219 |
6 202
|
mp1i |
|
220 |
154 6 84
|
divcli |
|
221 |
220
|
a1i |
|
222 |
219 221 145 148
|
divassd |
|
223 |
218 222
|
syl5eqr |
|
224 |
223
|
mpteq2dva |
|
225 |
204 214 224
|
3eqtr4d |
|
226 |
225
|
mptru |
|