Step |
Hyp |
Ref |
Expression |
1 |
|
atanval |
|
2 |
1
|
oveq2d |
|
3 |
|
ax-icn |
|
4 |
3
|
a1i |
|
5 |
|
halfcl |
|
6 |
3 5
|
mp1i |
|
7 |
|
ax-1cn |
|
8 |
|
atandm2 |
|
9 |
8
|
simp1bi |
|
10 |
|
mulcl |
|
11 |
3 9 10
|
sylancr |
|
12 |
|
subcl |
|
13 |
7 11 12
|
sylancr |
|
14 |
8
|
simp2bi |
|
15 |
13 14
|
logcld |
|
16 |
|
addcl |
|
17 |
7 11 16
|
sylancr |
|
18 |
8
|
simp3bi |
|
19 |
17 18
|
logcld |
|
20 |
15 19
|
subcld |
|
21 |
4 6 20
|
mulassd |
|
22 |
|
2cn |
|
23 |
|
2ne0 |
|
24 |
|
divneg |
|
25 |
7 22 23 24
|
mp3an |
|
26 |
|
ixi |
|
27 |
26
|
oveq1i |
|
28 |
3 3 22 23
|
divassi |
|
29 |
25 27 28
|
3eqtr2i |
|
30 |
29
|
oveq1i |
|
31 |
|
halfcn |
|
32 |
|
mulneg12 |
|
33 |
31 20 32
|
sylancr |
|
34 |
15 19
|
negsubdi2d |
|
35 |
34
|
oveq2d |
|
36 |
31
|
a1i |
|
37 |
36 19 15
|
subdid |
|
38 |
33 35 37
|
3eqtrd |
|
39 |
30 38
|
eqtr3id |
|
40 |
2 21 39
|
3eqtr2d |
|
41 |
40
|
fveq2d |
|
42 |
|
mulcl |
|
43 |
31 19 42
|
sylancr |
|
44 |
|
mulcl |
|
45 |
31 15 44
|
sylancr |
|
46 |
|
efsub |
|
47 |
43 45 46
|
syl2anc |
|
48 |
17 18 36
|
cxpefd |
|
49 |
|
cxpsqrt |
|
50 |
17 49
|
syl |
|
51 |
48 50
|
eqtr3d |
|
52 |
13 14 36
|
cxpefd |
|
53 |
|
cxpsqrt |
|
54 |
13 53
|
syl |
|
55 |
52 54
|
eqtr3d |
|
56 |
51 55
|
oveq12d |
|
57 |
41 47 56
|
3eqtrd |
|