Step |
Hyp |
Ref |
Expression |
1 |
|
cnelprrecn |
|
2 |
1
|
a1i |
|
3 |
|
ax-icn |
|
4 |
3
|
a1i |
|
5 |
|
simpr |
|
6 |
4 5
|
mulcld |
|
7 |
|
efcl |
|
8 |
6 7
|
syl |
|
9 |
|
ine0 |
|
10 |
9
|
a1i |
|
11 |
8 4 10
|
divcld |
|
12 |
|
negicn |
|
13 |
|
mulcl |
|
14 |
12 5 13
|
sylancr |
|
15 |
|
efcl |
|
16 |
14 15
|
syl |
|
17 |
16 4 10
|
divcld |
|
18 |
17
|
negcld |
|
19 |
11 18
|
addcld |
|
20 |
8 16
|
addcld |
|
21 |
8 4
|
mulcld |
|
22 |
|
efcl |
|
23 |
22
|
adantl |
|
24 |
|
1cnd |
|
25 |
2
|
dvmptid |
|
26 |
3
|
a1i |
|
27 |
2 5 24 25 26
|
dvmptcmul |
|
28 |
3
|
mulid1i |
|
29 |
28
|
mpteq2i |
|
30 |
27 29
|
eqtrdi |
|
31 |
|
eff |
|
32 |
31
|
a1i |
|
33 |
32
|
feqmptd |
|
34 |
33
|
oveq2d |
|
35 |
|
dvef |
|
36 |
35 33
|
syl5eq |
|
37 |
34 36
|
eqtr3d |
|
38 |
|
fveq2 |
|
39 |
2 2 6 4 23 23 30 37 38 38
|
dvmptco |
|
40 |
9
|
a1i |
|
41 |
2 8 21 39 26 40
|
dvmptdivc |
|
42 |
8 4 10
|
divcan4d |
|
43 |
42
|
mpteq2dva |
|
44 |
41 43
|
eqtrd |
|
45 |
|
mulcl |
|
46 |
16 12 45
|
sylancl |
|
47 |
46 4 10
|
divcld |
|
48 |
12
|
a1i |
|
49 |
12
|
a1i |
|
50 |
2 5 24 25 49
|
dvmptcmul |
|
51 |
12
|
mulid1i |
|
52 |
51
|
mpteq2i |
|
53 |
50 52
|
eqtrdi |
|
54 |
|
fveq2 |
|
55 |
2 2 14 48 23 23 53 37 54 54
|
dvmptco |
|
56 |
2 16 46 55 26 40
|
dvmptdivc |
|
57 |
2 17 47 56
|
dvmptneg |
|
58 |
46 4 10
|
divneg2d |
|
59 |
3 9
|
negne0i |
|
60 |
59
|
a1i |
|
61 |
16 48 60
|
divcan4d |
|
62 |
58 61
|
eqtrd |
|
63 |
62
|
mpteq2dva |
|
64 |
57 63
|
eqtrd |
|
65 |
2 11 8 44 18 16 64
|
dvmptadd |
|
66 |
|
2cnd |
|
67 |
|
2ne0 |
|
68 |
67
|
a1i |
|
69 |
2 19 20 65 66 68
|
dvmptdivc |
|
70 |
|
df-sin |
|
71 |
8 16
|
subcld |
|
72 |
|
2cnd |
|
73 |
67
|
a1i |
|
74 |
71 4 72 10 73
|
divdiv1d |
|
75 |
|
2cn |
|
76 |
3 75
|
mulcomi |
|
77 |
76
|
oveq2i |
|
78 |
74 77
|
eqtrdi |
|
79 |
8 16 4 10
|
divsubdird |
|
80 |
11 17
|
negsubd |
|
81 |
79 80
|
eqtr4d |
|
82 |
81
|
oveq1d |
|
83 |
78 82
|
eqtr3d |
|
84 |
83
|
mpteq2dva |
|
85 |
70 84
|
syl5eq |
|
86 |
85
|
oveq2d |
|
87 |
|
df-cos |
|
88 |
87
|
a1i |
|
89 |
69 86 88
|
3eqtr4d |
|
90 |
21 46
|
addcld |
|
91 |
2 8 21 39 16 46 55
|
dvmptadd |
|
92 |
2 20 90 91 66 68
|
dvmptdivc |
|
93 |
88
|
oveq2d |
|
94 |
71 4 10
|
divcld |
|
95 |
94 72 73
|
divnegd |
|
96 |
|
sinval |
|
97 |
96
|
adantl |
|
98 |
97 78
|
eqtr4d |
|
99 |
98
|
negeqd |
|
100 |
3
|
negnegi |
|
101 |
100
|
oveq2i |
|
102 |
|
mulneg2 |
|
103 |
71 12 102
|
sylancl |
|
104 |
101 103
|
syl5eqr |
|
105 |
|
mulcl |
|
106 |
16 3 105
|
sylancl |
|
107 |
21 106
|
negsubd |
|
108 |
|
mulneg2 |
|
109 |
16 3 108
|
sylancl |
|
110 |
109
|
oveq2d |
|
111 |
8 16 4
|
subdird |
|
112 |
107 110 111
|
3eqtr4d |
|
113 |
71 4 10
|
divrecd |
|
114 |
|
irec |
|
115 |
114
|
oveq2i |
|
116 |
113 115
|
eqtrdi |
|
117 |
116
|
negeqd |
|
118 |
104 112 117
|
3eqtr4d |
|
119 |
118
|
oveq1d |
|
120 |
95 99 119
|
3eqtr4d |
|
121 |
120
|
mpteq2dva |
|
122 |
92 93 121
|
3eqtr4d |
|
123 |
89 122
|
jca |
|
124 |
123
|
mptru |
|