Step |
Hyp |
Ref |
Expression |
1 |
|
rpre |
|
2 |
|
atanrecl |
|
3 |
1 2
|
syl |
|
4 |
|
picn |
|
5 |
|
2cn |
|
6 |
|
2ne0 |
|
7 |
|
divneg |
|
8 |
4 5 6 7
|
mp3an |
|
9 |
|
ax-1cn |
|
10 |
|
ax-icn |
|
11 |
1
|
recnd |
|
12 |
|
mulcl |
|
13 |
10 11 12
|
sylancr |
|
14 |
|
addcl |
|
15 |
9 13 14
|
sylancr |
|
16 |
|
atanre |
|
17 |
1 16
|
syl |
|
18 |
|
atandm2 |
|
19 |
17 18
|
sylib |
|
20 |
19
|
simp3d |
|
21 |
15 20
|
logcld |
|
22 |
|
subcl |
|
23 |
9 13 22
|
sylancr |
|
24 |
19
|
simp2d |
|
25 |
23 24
|
logcld |
|
26 |
21 25
|
subcld |
|
27 |
|
imre |
|
28 |
26 27
|
syl |
|
29 |
|
atanval |
|
30 |
17 29
|
syl |
|
31 |
30
|
oveq2d |
|
32 |
10 5 6
|
divcan2i |
|
33 |
32
|
oveq1i |
|
34 |
|
2re |
|
35 |
34
|
a1i |
|
36 |
35
|
recnd |
|
37 |
|
halfcl |
|
38 |
10 37
|
mp1i |
|
39 |
25 21
|
subcld |
|
40 |
36 38 39
|
mulassd |
|
41 |
33 40
|
eqtr3id |
|
42 |
31 41
|
eqtr4d |
|
43 |
21 25
|
negsubdi2d |
|
44 |
43
|
oveq2d |
|
45 |
42 44
|
eqtr4d |
|
46 |
|
mulneg12 |
|
47 |
10 26 46
|
sylancr |
|
48 |
45 47
|
eqtr4d |
|
49 |
48
|
fveq2d |
|
50 |
|
remulcl |
|
51 |
34 3 50
|
sylancr |
|
52 |
51
|
rered |
|
53 |
28 49 52
|
3eqtr2rd |
|
54 |
|
rpgt0 |
|
55 |
1
|
rered |
|
56 |
54 55
|
breqtrrd |
|
57 |
|
atanlogsublem |
|
58 |
17 56 57
|
syl2anc |
|
59 |
53 58
|
eqeltrd |
|
60 |
|
eliooord |
|
61 |
59 60
|
syl |
|
62 |
61
|
simpld |
|
63 |
|
pire |
|
64 |
63
|
renegcli |
|
65 |
64
|
a1i |
|
66 |
|
2pos |
|
67 |
66
|
a1i |
|
68 |
|
ltdivmul |
|
69 |
65 3 35 67 68
|
syl112anc |
|
70 |
62 69
|
mpbird |
|
71 |
8 70
|
eqbrtrid |
|
72 |
61
|
simprd |
|
73 |
63
|
a1i |
|
74 |
|
ltmuldiv2 |
|
75 |
3 73 35 67 74
|
syl112anc |
|
76 |
72 75
|
mpbid |
|
77 |
|
halfpire |
|
78 |
77
|
renegcli |
|
79 |
78
|
rexri |
|
80 |
77
|
rexri |
|
81 |
|
elioo2 |
|
82 |
79 80 81
|
mp2an |
|
83 |
3 71 76 82
|
syl3anbrc |
|