Step |
Hyp |
Ref |
Expression |
1 |
|
0lt1 |
|
2 |
|
0re |
|
3 |
|
1re |
|
4 |
2 3
|
ltnsymi |
|
5 |
1 4
|
ax-mp |
|
6 |
|
lt0neg1 |
|
7 |
3 6
|
ax-mp |
|
8 |
5 7
|
mtbi |
|
9 |
|
pire |
|
10 |
9
|
rehalfcli |
|
11 |
|
2re |
|
12 |
|
pipos |
|
13 |
|
2pos |
|
14 |
9 11 12 13
|
divgt0ii |
|
15 |
|
4re |
|
16 |
|
pigt2lt4 |
|
17 |
16
|
simpri |
|
18 |
9 15 17
|
ltleii |
|
19 |
11 13
|
pm3.2i |
|
20 |
|
ledivmul |
|
21 |
9 11 19 20
|
mp3an |
|
22 |
|
2t2e4 |
|
23 |
22
|
breq2i |
|
24 |
21 23
|
bitr2i |
|
25 |
18 24
|
mpbi |
|
26 |
|
0xr |
|
27 |
|
elioc2 |
|
28 |
26 11 27
|
mp2an |
|
29 |
10 14 25 28
|
mpbir3an |
|
30 |
|
sin02gt0 |
|
31 |
29 30
|
ax-mp |
|
32 |
|
breq2 |
|
33 |
31 32
|
mpbii |
|
34 |
8 33
|
mto |
|
35 |
|
sq1 |
|
36 |
|
resincl |
|
37 |
10 36
|
ax-mp |
|
38 |
37 31
|
gt0ne0ii |
|
39 |
38
|
neii |
|
40 |
|
2ne0 |
|
41 |
40
|
neii |
|
42 |
9
|
recni |
|
43 |
|
2cn |
|
44 |
42 43 40
|
divcan2i |
|
45 |
44
|
fveq2i |
|
46 |
10
|
recni |
|
47 |
|
sin2t |
|
48 |
46 47
|
ax-mp |
|
49 |
45 48
|
eqtr3i |
|
50 |
|
sinpi |
|
51 |
49 50
|
eqtr3i |
|
52 |
|
sincl |
|
53 |
46 52
|
ax-mp |
|
54 |
|
coscl |
|
55 |
46 54
|
ax-mp |
|
56 |
53 55
|
mulcli |
|
57 |
43 56
|
mul0ori |
|
58 |
51 57
|
mpbi |
|
59 |
41 58
|
mtpor |
|
60 |
53 55
|
mul0ori |
|
61 |
59 60
|
mpbi |
|
62 |
39 61
|
mtpor |
|
63 |
62
|
oveq1i |
|
64 |
|
sq0 |
|
65 |
63 64
|
eqtri |
|
66 |
65
|
oveq2i |
|
67 |
|
sincossq |
|
68 |
46 67
|
ax-mp |
|
69 |
66 68
|
eqtr3i |
|
70 |
53
|
sqcli |
|
71 |
70
|
addid1i |
|
72 |
35 69 71
|
3eqtr2ri |
|
73 |
|
ax-1cn |
|
74 |
53 73
|
sqeqori |
|
75 |
72 74
|
mpbi |
|
76 |
75
|
ori |
|
77 |
34 76
|
mt3 |
|
78 |
77 62
|
pm3.2i |
|