Step |
Hyp |
Ref |
Expression |
1 |
|
tan4thpi |
|
2 |
1
|
fveq2i |
|
3 |
|
pire |
|
4 |
|
4nn |
|
5 |
|
nndivre |
|
6 |
3 4 5
|
mp2an |
|
7 |
6
|
recni |
|
8 |
|
rere |
|
9 |
6 8
|
ax-mp |
|
10 |
|
pirp |
|
11 |
|
rphalfcl |
|
12 |
10 11
|
ax-mp |
|
13 |
|
rpgt0 |
|
14 |
12 13
|
ax-mp |
|
15 |
|
halfpire |
|
16 |
|
lt0neg2 |
|
17 |
15 16
|
ax-mp |
|
18 |
14 17
|
mpbi |
|
19 |
|
nnrp |
|
20 |
4 19
|
ax-mp |
|
21 |
|
rpdivcl |
|
22 |
10 20 21
|
mp2an |
|
23 |
|
rpgt0 |
|
24 |
22 23
|
ax-mp |
|
25 |
|
neghalfpire |
|
26 |
|
0re |
|
27 |
25 26 6
|
lttri |
|
28 |
18 24 27
|
mp2an |
|
29 |
3
|
recni |
|
30 |
|
2cnne0 |
|
31 |
|
divdiv1 |
|
32 |
29 30 30 31
|
mp3an |
|
33 |
|
2t2e4 |
|
34 |
33
|
oveq2i |
|
35 |
32 34
|
eqtri |
|
36 |
|
rphalflt |
|
37 |
12 36
|
ax-mp |
|
38 |
35 37
|
eqbrtrri |
|
39 |
25
|
rexri |
|
40 |
15
|
rexri |
|
41 |
|
elioo2 |
|
42 |
39 40 41
|
mp2an |
|
43 |
6 28 38 42
|
mpbir3an |
|
44 |
9 43
|
eqeltri |
|
45 |
|
atantan |
|
46 |
7 44 45
|
mp2an |
|
47 |
2 46
|
eqtr3i |
|