Step |
Hyp |
Ref |
Expression |
1 |
|
asincl |
|
2 |
|
sinval |
|
3 |
1 2
|
syl |
|
4 |
|
ax-icn |
|
5 |
|
mulcl |
|
6 |
4 5
|
mpan |
|
7 |
6
|
negcld |
|
8 |
|
ax-1cn |
|
9 |
|
sqcl |
|
10 |
|
subcl |
|
11 |
8 9 10
|
sylancr |
|
12 |
11
|
sqrtcld |
|
13 |
6 7 12
|
pnpcan2d |
|
14 |
|
efiasin |
|
15 |
|
mulneg12 |
|
16 |
4 1 15
|
sylancr |
|
17 |
|
asinneg |
|
18 |
17
|
oveq2d |
|
19 |
16 18
|
eqtr4d |
|
20 |
19
|
fveq2d |
|
21 |
|
negcl |
|
22 |
|
efiasin |
|
23 |
21 22
|
syl |
|
24 |
|
mulneg2 |
|
25 |
4 24
|
mpan |
|
26 |
|
sqneg |
|
27 |
26
|
oveq2d |
|
28 |
27
|
fveq2d |
|
29 |
25 28
|
oveq12d |
|
30 |
20 23 29
|
3eqtrd |
|
31 |
14 30
|
oveq12d |
|
32 |
6
|
2timesd |
|
33 |
|
2cn |
|
34 |
|
mulass |
|
35 |
33 4 34
|
mp3an12 |
|
36 |
6 6
|
subnegd |
|
37 |
32 35 36
|
3eqtr4d |
|
38 |
13 31 37
|
3eqtr4d |
|
39 |
|
mulcl |
|
40 |
4 1 39
|
sylancr |
|
41 |
|
efcl |
|
42 |
40 41
|
syl |
|
43 |
|
negicn |
|
44 |
|
mulcl |
|
45 |
43 1 44
|
sylancr |
|
46 |
|
efcl |
|
47 |
45 46
|
syl |
|
48 |
42 47
|
subcld |
|
49 |
|
id |
|
50 |
|
2mulicn |
|
51 |
50
|
a1i |
|
52 |
|
2muline0 |
|
53 |
52
|
a1i |
|
54 |
48 49 51 53
|
divmul2d |
|
55 |
38 54
|
mpbird |
|
56 |
3 55
|
eqtrd |
|