Step |
Hyp |
Ref |
Expression |
1 |
|
0red |
|
2 |
|
imcl |
|
3 |
|
ax-icn |
|
4 |
|
negcl |
|
5 |
4
|
adantr |
|
6 |
|
mulcl |
|
7 |
3 5 6
|
sylancr |
|
8 |
|
ax-1cn |
|
9 |
5
|
sqcld |
|
10 |
|
subcl |
|
11 |
8 9 10
|
sylancr |
|
12 |
11
|
sqrtcld |
|
13 |
7 12
|
addcld |
|
14 |
|
asinlem |
|
15 |
5 14
|
syl |
|
16 |
13 15
|
absrpcld |
|
17 |
|
2z |
|
18 |
|
rpexpcl |
|
19 |
16 17 18
|
sylancl |
|
20 |
19
|
rprecred |
|
21 |
13
|
cjcld |
|
22 |
21
|
recld |
|
23 |
19
|
rpreccld |
|
24 |
23
|
rpge0d |
|
25 |
|
imneg |
|
26 |
25
|
adantr |
|
27 |
2
|
le0neg2d |
|
28 |
27
|
biimpa |
|
29 |
26 28
|
eqbrtrd |
|
30 |
|
asinlem3a |
|
31 |
5 29 30
|
syl2anc |
|
32 |
13
|
recjd |
|
33 |
31 32
|
breqtrrd |
|
34 |
20 22 24 33
|
mulge0d |
|
35 |
|
recval |
|
36 |
13 15 35
|
syl2anc |
|
37 |
|
asinlem2 |
|
38 |
37
|
adantr |
|
39 |
38
|
eqcomd |
|
40 |
|
1cnd |
|
41 |
|
simpl |
|
42 |
|
mulcl |
|
43 |
3 41 42
|
sylancr |
|
44 |
|
sqcl |
|
45 |
44
|
adantr |
|
46 |
|
subcl |
|
47 |
8 45 46
|
sylancr |
|
48 |
47
|
sqrtcld |
|
49 |
43 48
|
addcld |
|
50 |
40 49 13 15
|
divmul3d |
|
51 |
39 50
|
mpbird |
|
52 |
19
|
rpcnd |
|
53 |
19
|
rpne0d |
|
54 |
21 52 53
|
divrec2d |
|
55 |
36 51 54
|
3eqtr3d |
|
56 |
55
|
fveq2d |
|
57 |
20 21
|
remul2d |
|
58 |
56 57
|
eqtrd |
|
59 |
34 58
|
breqtrrd |
|
60 |
|
asinlem3a |
|
61 |
1 2 59 60
|
lecasei |
|