Step |
Hyp |
Ref |
Expression |
1 |
|
2t1e2 |
|
2 |
|
df-2 |
|
3 |
1 2
|
eqtr2i |
|
4 |
|
zcn |
|
5 |
|
2cn |
|
6 |
|
picn |
|
7 |
|
mul12 |
|
8 |
5 6 7
|
mp3an23 |
|
9 |
4 8
|
syl |
|
10 |
9
|
fveq2d |
|
11 |
|
cos2kpi |
|
12 |
|
zre |
|
13 |
|
pire |
|
14 |
|
remulcl |
|
15 |
12 13 14
|
sylancl |
|
16 |
15
|
recnd |
|
17 |
|
cos2t |
|
18 |
16 17
|
syl |
|
19 |
10 11 18
|
3eqtr3rd |
|
20 |
15
|
recoscld |
|
21 |
20
|
recnd |
|
22 |
21
|
sqcld |
|
23 |
|
mulcl |
|
24 |
5 22 23
|
sylancr |
|
25 |
|
ax-1cn |
|
26 |
|
subadd |
|
27 |
25 25 26
|
mp3an23 |
|
28 |
24 27
|
syl |
|
29 |
19 28
|
mpbid |
|
30 |
3 29
|
syl5reqr |
|
31 |
|
2cnne0 |
|
32 |
|
mulcan |
|
33 |
25 31 32
|
mp3an23 |
|
34 |
22 33
|
syl |
|
35 |
30 34
|
mpbid |
|
36 |
|
sq1 |
|
37 |
35 36
|
eqtr4di |
|
38 |
|
1re |
|
39 |
|
sqabs |
|
40 |
20 38 39
|
sylancl |
|
41 |
37 40
|
mpbid |
|
42 |
|
abs1 |
|
43 |
41 42
|
eqtrdi |
|