Step |
Hyp |
Ref |
Expression |
1 |
|
df-tan |
|
2 |
|
cnvimass |
|
3 |
|
cosf |
|
4 |
3
|
fdmi |
|
5 |
2 4
|
sseqtri |
|
6 |
5
|
sseli |
|
7 |
6
|
sincld |
|
8 |
6
|
coscld |
|
9 |
|
ffn |
|
10 |
|
elpreima |
|
11 |
3 9 10
|
mp2b |
|
12 |
|
eldifsni |
|
13 |
12
|
adantl |
|
14 |
11 13
|
sylbi |
|
15 |
7 8 14
|
divrecd |
|
16 |
15
|
mpteq2ia |
|
17 |
1 16
|
eqtri |
|
18 |
17
|
oveq2i |
|
19 |
|
cnelprrecn |
|
20 |
19
|
a1i |
|
21 |
|
difss |
|
22 |
|
imass2 |
|
23 |
21 22
|
ax-mp |
|
24 |
|
fimacnv |
|
25 |
3 24
|
ax-mp |
|
26 |
23 25
|
sseqtri |
|
27 |
26
|
sseli |
|
28 |
27
|
sincld |
|
29 |
28
|
adantl |
|
30 |
8
|
adantl |
|
31 |
|
sincl |
|
32 |
31
|
adantl |
|
33 |
|
coscl |
|
34 |
33
|
adantl |
|
35 |
|
dvsin |
|
36 |
|
sinf |
|
37 |
36
|
a1i |
|
38 |
37
|
feqmptd |
|
39 |
38
|
oveq2d |
|
40 |
3
|
a1i |
|
41 |
40
|
feqmptd |
|
42 |
35 39 41
|
3eqtr3a |
|
43 |
26
|
a1i |
|
44 |
|
eqid |
|
45 |
44
|
cnfldtopon |
|
46 |
45
|
toponrestid |
|
47 |
|
dvtanlem |
|
48 |
47
|
a1i |
|
49 |
20 32 34 42 43 46 44 48
|
dvmptres |
|
50 |
8 14
|
reccld |
|
51 |
50
|
adantl |
|
52 |
|
ovexd |
|
53 |
11
|
simprbi |
|
54 |
53
|
adantl |
|
55 |
29
|
negcld |
|
56 |
|
eldifi |
|
57 |
|
eldifsni |
|
58 |
56 57
|
reccld |
|
59 |
58
|
adantl |
|
60 |
|
negex |
|
61 |
60
|
a1i |
|
62 |
32
|
negcld |
|
63 |
41
|
oveq2d |
|
64 |
|
dvcos |
|
65 |
63 64
|
eqtr3di |
|
66 |
20 34 62 65 43 46 44 48
|
dvmptres |
|
67 |
|
ax-1cn |
|
68 |
|
dvrec |
|
69 |
67 68
|
mp1i |
|
70 |
|
oveq2 |
|
71 |
|
oveq1 |
|
72 |
71
|
oveq2d |
|
73 |
72
|
negeqd |
|
74 |
20 20 54 55 59 61 66 69 70 73
|
dvmptco |
|
75 |
20 29 30 49 51 52 74
|
dvmptmul |
|
76 |
75
|
mptru |
|
77 |
|
ovex |
|
78 |
77 1
|
dmmpti |
|
79 |
78
|
eqcomi |
|
80 |
8
|
sqcld |
|
81 |
7
|
sqcld |
|
82 |
|
sqne0 |
|
83 |
8 82
|
syl |
|
84 |
14 83
|
mpbird |
|
85 |
80 81 80 84
|
divdird |
|
86 |
80 81
|
addcomd |
|
87 |
|
sincossq |
|
88 |
6 87
|
syl |
|
89 |
86 88
|
eqtrd |
|
90 |
89
|
oveq1d |
|
91 |
85 90
|
eqtr3d |
|
92 |
8 14
|
recidd |
|
93 |
80 84
|
dividd |
|
94 |
92 93
|
eqtr4d |
|
95 |
7 7 80 84
|
div23d |
|
96 |
7
|
sqvald |
|
97 |
96
|
oveq1d |
|
98 |
80 84
|
reccld |
|
99 |
98 7
|
mul2negd |
|
100 |
7 80 84
|
divrec2d |
|
101 |
99 100
|
eqtr4d |
|
102 |
101
|
oveq1d |
|
103 |
95 97 102
|
3eqtr4rd |
|
104 |
94 103
|
oveq12d |
|
105 |
|
2nn0 |
|
106 |
|
expneg |
|
107 |
8 105 106
|
sylancl |
|
108 |
91 104 107
|
3eqtr4d |
|
109 |
108
|
rgen |
|
110 |
|
mpteq12 |
|
111 |
79 109 110
|
mp2an |
|
112 |
18 76 111
|
3eqtri |
|