Step |
Hyp |
Ref |
Expression |
1 |
|
atanre |
|
2 |
1
|
adantr |
|
3 |
|
atanneg |
|
4 |
2 3
|
syl |
|
5 |
|
renegcl |
|
6 |
5
|
adantr |
|
7 |
|
lt0neg1 |
|
8 |
7
|
biimpa |
|
9 |
6 8
|
elrpd |
|
10 |
|
atanbndlem |
|
11 |
9 10
|
syl |
|
12 |
4 11
|
eqeltrrd |
|
13 |
|
halfpire |
|
14 |
13
|
recni |
|
15 |
14
|
negnegi |
|
16 |
15
|
oveq2i |
|
17 |
12 16
|
eleqtrrdi |
|
18 |
|
neghalfpire |
|
19 |
|
atanrecl |
|
20 |
19
|
adantr |
|
21 |
|
iooneg |
|
22 |
18 13 20 21
|
mp3an12i |
|
23 |
17 22
|
mpbird |
|
24 |
|
simpr |
|
25 |
24
|
fveq2d |
|
26 |
|
atan0 |
|
27 |
25 26
|
eqtrdi |
|
28 |
|
0re |
|
29 |
|
pirp |
|
30 |
|
rphalfcl |
|
31 |
|
rpgt0 |
|
32 |
29 30 31
|
mp2b |
|
33 |
|
lt0neg2 |
|
34 |
13 33
|
ax-mp |
|
35 |
32 34
|
mpbi |
|
36 |
18
|
rexri |
|
37 |
13
|
rexri |
|
38 |
|
elioo2 |
|
39 |
36 37 38
|
mp2an |
|
40 |
28 35 32 39
|
mpbir3an |
|
41 |
27 40
|
eqeltrdi |
|
42 |
|
elrp |
|
43 |
|
atanbndlem |
|
44 |
42 43
|
sylbir |
|
45 |
|
lttri4 |
|
46 |
28 45
|
mpan2 |
|
47 |
23 41 44 46
|
mpjao3dan |
|