Step |
Hyp |
Ref |
Expression |
1 |
|
3re |
|
2 |
|
halfpire |
|
3 |
1 2
|
remulcli |
|
4 |
3
|
rexri |
|
5 |
|
2re |
|
6 |
|
pire |
|
7 |
5 6
|
remulcli |
|
8 |
7
|
rexri |
|
9 |
|
elioo2 |
|
10 |
4 8 9
|
mp2an |
|
11 |
|
df-3 |
|
12 |
11
|
oveq1i |
|
13 |
|
2cn |
|
14 |
|
ax-1cn |
|
15 |
2
|
recni |
|
16 |
13 14 15
|
adddiri |
|
17 |
6
|
recni |
|
18 |
|
2ne0 |
|
19 |
17 13 18
|
divcan2i |
|
20 |
15
|
mulid2i |
|
21 |
19 20
|
oveq12i |
|
22 |
12 16 21
|
3eqtrri |
|
23 |
22
|
breq1i |
|
24 |
|
ltaddsub |
|
25 |
6 2 24
|
mp3an12 |
|
26 |
23 25
|
bitr3id |
|
27 |
|
ltsubadd |
|
28 |
2 3 27
|
mp3an23 |
|
29 |
|
df-4 |
|
30 |
29
|
oveq1i |
|
31 |
1
|
recni |
|
32 |
31 14 15
|
adddiri |
|
33 |
20
|
oveq2i |
|
34 |
30 32 33
|
3eqtrri |
|
35 |
|
4cn |
|
36 |
|
2cnne0 |
|
37 |
|
div12 |
|
38 |
35 17 36 37
|
mp3an |
|
39 |
|
4d2e2 |
|
40 |
39
|
oveq2i |
|
41 |
17 13
|
mulcomi |
|
42 |
40 41
|
eqtri |
|
43 |
38 42
|
eqtri |
|
44 |
34 43
|
eqtri |
|
45 |
44
|
breq2i |
|
46 |
28 45
|
bitr2di |
|
47 |
26 46
|
anbi12d |
|
48 |
|
resubcl |
|
49 |
2 48
|
mpan2 |
|
50 |
6
|
rexri |
|
51 |
|
elioo2 |
|
52 |
50 4 51
|
mp2an |
|
53 |
|
sincosq3sgn |
|
54 |
52 53
|
sylbir |
|
55 |
49 54
|
syl3an1 |
|
56 |
55
|
3expib |
|
57 |
47 56
|
sylbid |
|
58 |
49
|
resincld |
|
59 |
58
|
lt0neg1d |
|
60 |
59
|
anbi1d |
|
61 |
57 60
|
sylibd |
|
62 |
|
recn |
|
63 |
|
pncan3 |
|
64 |
15 62 63
|
sylancr |
|
65 |
64
|
fveq2d |
|
66 |
49
|
recnd |
|
67 |
|
coshalfpip |
|
68 |
66 67
|
syl |
|
69 |
65 68
|
eqtr3d |
|
70 |
69
|
breq2d |
|
71 |
64
|
fveq2d |
|
72 |
|
sinhalfpip |
|
73 |
66 72
|
syl |
|
74 |
71 73
|
eqtr3d |
|
75 |
74
|
breq1d |
|
76 |
70 75
|
anbi12d |
|
77 |
61 76
|
sylibrd |
|
78 |
77
|
3impib |
|
79 |
78
|
ancomd |
|
80 |
10 79
|
sylbi |
|