Step |
Hyp |
Ref |
Expression |
1 |
|
elioore |
|
2 |
1
|
adantr |
|
3 |
2
|
renegcld |
|
4 |
1
|
lt0neg1d |
|
5 |
4
|
biimpa |
|
6 |
|
eliooord |
|
7 |
6
|
simpld |
|
8 |
7
|
adantr |
|
9 |
|
halfpire |
|
10 |
|
ltnegcon1 |
|
11 |
9 2 10
|
sylancr |
|
12 |
8 11
|
mpbid |
|
13 |
|
0xr |
|
14 |
9
|
rexri |
|
15 |
|
elioo2 |
|
16 |
13 14 15
|
mp2an |
|
17 |
3 5 12 16
|
syl3anbrc |
|
18 |
|
sincosq1sgn |
|
19 |
17 18
|
syl |
|
20 |
19
|
simprd |
|
21 |
20
|
gt0ne0d |
|
22 |
3 21
|
retancld |
|
23 |
|
tangtx |
|
24 |
17 23
|
syl |
|
25 |
3 22 24
|
ltled |
|
26 |
|
0re |
|
27 |
|
ltle |
|
28 |
1 26 27
|
sylancl |
|
29 |
28
|
imp |
|
30 |
2 29
|
absnidd |
|
31 |
1
|
recnd |
|
32 |
31
|
adantr |
|
33 |
32
|
negnegd |
|
34 |
33
|
fveq2d |
|
35 |
32
|
negcld |
|
36 |
|
tanneg |
|
37 |
35 21 36
|
syl2anc |
|
38 |
34 37
|
eqtr3d |
|
39 |
38
|
fveq2d |
|
40 |
22
|
recnd |
|
41 |
40
|
absnegd |
|
42 |
|
0red |
|
43 |
|
ltle |
|
44 |
26 3 43
|
sylancr |
|
45 |
5 44
|
mpd |
|
46 |
42 3 22 45 25
|
letrd |
|
47 |
22 46
|
absidd |
|
48 |
39 41 47
|
3eqtrd |
|
49 |
25 30 48
|
3brtr4d |
|
50 |
|
abs0 |
|
51 |
50 26
|
eqeltri |
|
52 |
51
|
leidi |
|
53 |
52
|
a1i |
|
54 |
|
simpr |
|
55 |
54
|
fveq2d |
|
56 |
54
|
fveq2d |
|
57 |
|
tan0 |
|
58 |
56 57
|
eqtrdi |
|
59 |
58
|
fveq2d |
|
60 |
53 55 59
|
3brtr4d |
|
61 |
1
|
adantr |
|
62 |
|
simpr |
|
63 |
6
|
simprd |
|
64 |
63
|
adantr |
|
65 |
|
elioo2 |
|
66 |
13 14 65
|
mp2an |
|
67 |
61 62 64 66
|
syl3anbrc |
|
68 |
|
sincosq1sgn |
|
69 |
67 68
|
syl |
|
70 |
69
|
simprd |
|
71 |
70
|
gt0ne0d |
|
72 |
61 71
|
retancld |
|
73 |
|
tangtx |
|
74 |
67 73
|
syl |
|
75 |
61 72 74
|
ltled |
|
76 |
|
ltle |
|
77 |
26 1 76
|
sylancr |
|
78 |
77
|
imp |
|
79 |
61 78
|
absidd |
|
80 |
|
0red |
|
81 |
80 61 72 78 75
|
letrd |
|
82 |
72 81
|
absidd |
|
83 |
75 79 82
|
3brtr4d |
|
84 |
|
lttri4 |
|
85 |
1 26 84
|
sylancl |
|
86 |
49 60 83 85
|
mpjao3dan |
|