Step |
Hyp |
Ref |
Expression |
1 |
|
simpl |
|
2 |
|
simpr |
|
3 |
|
fveq2 |
|
4 |
|
ax-icn |
|
5 |
4
|
renegi |
|
6 |
|
rei |
|
7 |
6
|
negeqi |
|
8 |
|
neg0 |
|
9 |
5 7 8
|
3eqtri |
|
10 |
3 9
|
eqtrdi |
|
11 |
10
|
necon3i |
|
12 |
2 11
|
syl |
|
13 |
|
fveq2 |
|
14 |
13 6
|
eqtrdi |
|
15 |
14
|
necon3i |
|
16 |
2 15
|
syl |
|
17 |
|
atandm |
|
18 |
1 12 16 17
|
syl3anbrc |
|
19 |
|
halfcl |
|
20 |
4 19
|
ax-mp |
|
21 |
|
ax-1cn |
|
22 |
|
mulcl |
|
23 |
4 1 22
|
sylancr |
|
24 |
|
subcl |
|
25 |
21 23 24
|
sylancr |
|
26 |
|
atandm2 |
|
27 |
18 26
|
sylib |
|
28 |
27
|
simp2d |
|
29 |
25 28
|
logcld |
|
30 |
|
addcl |
|
31 |
21 23 30
|
sylancr |
|
32 |
27
|
simp3d |
|
33 |
31 32
|
logcld |
|
34 |
29 33
|
subcld |
|
35 |
|
cjmul |
|
36 |
20 34 35
|
sylancr |
|
37 |
|
2ne0 |
|
38 |
|
2cn |
|
39 |
4 38
|
cjdivi |
|
40 |
37 39
|
ax-mp |
|
41 |
|
divneg |
|
42 |
4 38 37 41
|
mp3an |
|
43 |
|
cji |
|
44 |
|
2re |
|
45 |
|
cjre |
|
46 |
44 45
|
ax-mp |
|
47 |
43 46
|
oveq12i |
|
48 |
42 47
|
eqtr4i |
|
49 |
40 48
|
eqtr4i |
|
50 |
49
|
oveq1i |
|
51 |
34
|
cjcld |
|
52 |
|
mulneg12 |
|
53 |
20 51 52
|
sylancr |
|
54 |
50 53
|
syl5eq |
|
55 |
|
cjsub |
|
56 |
29 33 55
|
syl2anc |
|
57 |
|
imsub |
|
58 |
21 23 57
|
sylancr |
|
59 |
|
reim |
|
60 |
59
|
adantr |
|
61 |
60
|
oveq2d |
|
62 |
58 61
|
eqtr4d |
|
63 |
|
df-neg |
|
64 |
|
im1 |
|
65 |
64
|
oveq1i |
|
66 |
63 65
|
eqtr4i |
|
67 |
62 66
|
eqtr4di |
|
68 |
|
recl |
|
69 |
68
|
adantr |
|
70 |
69
|
recnd |
|
71 |
70 2
|
negne0d |
|
72 |
67 71
|
eqnetrd |
|
73 |
|
logcj |
|
74 |
25 72 73
|
syl2anc |
|
75 |
|
cjsub |
|
76 |
21 23 75
|
sylancr |
|
77 |
|
1re |
|
78 |
|
cjre |
|
79 |
77 78
|
mp1i |
|
80 |
|
cjmul |
|
81 |
4 1 80
|
sylancr |
|
82 |
43
|
oveq1i |
|
83 |
|
cjcl |
|
84 |
83
|
adantr |
|
85 |
|
mulneg1 |
|
86 |
4 84 85
|
sylancr |
|
87 |
82 86
|
syl5eq |
|
88 |
81 87
|
eqtrd |
|
89 |
79 88
|
oveq12d |
|
90 |
|
mulcl |
|
91 |
4 84 90
|
sylancr |
|
92 |
|
subneg |
|
93 |
21 91 92
|
sylancr |
|
94 |
76 89 93
|
3eqtrd |
|
95 |
94
|
fveq2d |
|
96 |
74 95
|
eqtr3d |
|
97 |
|
imadd |
|
98 |
21 23 97
|
sylancr |
|
99 |
60
|
oveq2d |
|
100 |
64
|
oveq1i |
|
101 |
99 100
|
eqtr4di |
|
102 |
70
|
addid2d |
|
103 |
98 101 102
|
3eqtr2d |
|
104 |
103 2
|
eqnetrd |
|
105 |
|
logcj |
|
106 |
31 104 105
|
syl2anc |
|
107 |
|
cjadd |
|
108 |
21 23 107
|
sylancr |
|
109 |
79 88
|
oveq12d |
|
110 |
|
negsub |
|
111 |
21 91 110
|
sylancr |
|
112 |
108 109 111
|
3eqtrd |
|
113 |
112
|
fveq2d |
|
114 |
106 113
|
eqtr3d |
|
115 |
96 114
|
oveq12d |
|
116 |
56 115
|
eqtrd |
|
117 |
116
|
negeqd |
|
118 |
|
addcl |
|
119 |
21 91 118
|
sylancr |
|
120 |
|
atandmcj |
|
121 |
18 120
|
syl |
|
122 |
|
atandm2 |
|
123 |
122
|
simp3bi |
|
124 |
121 123
|
syl |
|
125 |
119 124
|
logcld |
|
126 |
|
subcl |
|
127 |
21 91 126
|
sylancr |
|
128 |
122
|
simp2bi |
|
129 |
121 128
|
syl |
|
130 |
127 129
|
logcld |
|
131 |
125 130
|
negsubdi2d |
|
132 |
117 131
|
eqtrd |
|
133 |
132
|
oveq2d |
|
134 |
36 54 133
|
3eqtrd |
|
135 |
|
atanval |
|
136 |
18 135
|
syl |
|
137 |
136
|
fveq2d |
|
138 |
|
atanval |
|
139 |
121 138
|
syl |
|
140 |
134 137 139
|
3eqtr4d |
|
141 |
18 140
|
jca |
|