Step |
Hyp |
Ref |
Expression |
1 |
|
atancl |
|
2 |
|
2efiatan |
|
3 |
2
|
oveq1d |
|
4 |
|
2mulicn |
|
5 |
4
|
a1i |
|
6 |
|
atandm |
|
7 |
6
|
simp1bi |
|
8 |
|
ax-icn |
|
9 |
|
addcl |
|
10 |
7 8 9
|
sylancl |
|
11 |
|
subneg |
|
12 |
7 8 11
|
sylancl |
|
13 |
6
|
simp2bi |
|
14 |
8
|
negcli |
|
15 |
|
subeq0 |
|
16 |
15
|
necon3bid |
|
17 |
7 14 16
|
sylancl |
|
18 |
13 17
|
mpbird |
|
19 |
12 18
|
eqnetrrd |
|
20 |
5 10 19
|
divcld |
|
21 |
|
ax-1cn |
|
22 |
|
npcan |
|
23 |
20 21 22
|
sylancl |
|
24 |
3 23
|
eqtrd |
|
25 |
|
2muline0 |
|
26 |
25
|
a1i |
|
27 |
5 10 26 19
|
divne0d |
|
28 |
24 27
|
eqnetrd |
|
29 |
|
tanval3 |
|
30 |
1 28 29
|
syl2anc |
|
31 |
2
|
oveq1d |
|
32 |
21
|
a1i |
|
33 |
20 32 32
|
subsub4d |
|
34 |
|
df-2 |
|
35 |
34
|
oveq2i |
|
36 |
33 35
|
eqtr4di |
|
37 |
31 36
|
eqtrd |
|
38 |
|
2cn |
|
39 |
|
mulcl |
|
40 |
38 10 39
|
sylancr |
|
41 |
5 40 10 19
|
divsubdird |
|
42 |
|
mulneg12 |
|
43 |
38 7 42
|
sylancr |
|
44 |
|
negsub |
|
45 |
8 7 44
|
sylancr |
|
46 |
45
|
oveq1d |
|
47 |
7
|
negcld |
|
48 |
|
pncan2 |
|
49 |
8 47 48
|
sylancr |
|
50 |
8
|
a1i |
|
51 |
50 7 50
|
subsub4d |
|
52 |
46 49 51
|
3eqtr3rd |
|
53 |
52
|
oveq2d |
|
54 |
38
|
a1i |
|
55 |
54 50 10
|
subdid |
|
56 |
43 53 55
|
3eqtr2rd |
|
57 |
56
|
oveq1d |
|
58 |
54 10 19
|
divcan4d |
|
59 |
58
|
oveq2d |
|
60 |
41 57 59
|
3eqtr3d |
|
61 |
37 60
|
eqtr4d |
|
62 |
24
|
oveq2d |
|
63 |
8 38 8
|
mul12i |
|
64 |
|
ixi |
|
65 |
64
|
oveq2i |
|
66 |
21
|
negcli |
|
67 |
38
|
mulm1i |
|
68 |
66 38 67
|
mulcomli |
|
69 |
63 65 68
|
3eqtri |
|
70 |
69
|
oveq1i |
|
71 |
50 5 10 19
|
divassd |
|
72 |
70 71
|
eqtr3id |
|
73 |
62 72
|
eqtr4d |
|
74 |
61 73
|
oveq12d |
|
75 |
38
|
negcli |
|
76 |
|
mulcl |
|
77 |
75 7 76
|
sylancr |
|
78 |
75
|
a1i |
|
79 |
|
2ne0 |
|
80 |
38 79
|
negne0i |
|
81 |
80
|
a1i |
|
82 |
77 78 10 81 19
|
divcan7d |
|
83 |
7 78 81
|
divcan3d |
|
84 |
82 83
|
eqtrd |
|
85 |
74 84
|
eqtrd |
|
86 |
30 85
|
eqtrd |
|