Step |
Hyp |
Ref |
Expression |
1 |
|
recn |
|
2 |
1
|
negnegd |
|
3 |
2
|
adantr |
|
4 |
3
|
eqcomd |
|
5 |
4
|
fveq2d |
|
6 |
|
simpl |
|
7 |
6
|
renegcld |
|
8 |
|
0re |
|
9 |
|
ltle |
|
10 |
8 9
|
mpan2 |
|
11 |
10
|
imp |
|
12 |
|
le0neg1 |
|
13 |
12
|
adantr |
|
14 |
11 13
|
mpbid |
|
15 |
7 14
|
sqrtnegd |
|
16 |
5 15
|
eqtrd |
|
17 |
|
ax-icn |
|
18 |
17
|
a1i |
|
19 |
1
|
adantr |
|
20 |
19
|
negcld |
|
21 |
20
|
sqrtcld |
|
22 |
18 21
|
mulcomd |
|
23 |
7 14
|
resqrtcld |
|
24 |
|
inelr |
|
25 |
24
|
a1i |
|
26 |
18 25
|
eldifd |
|
27 |
|
lt0neg1 |
|
28 |
8
|
a1i |
|
29 |
|
ltne |
|
30 |
28 29
|
sylan |
|
31 |
|
simpl |
|
32 |
31
|
renegcld |
|
33 |
10 27 12
|
3imtr3d |
|
34 |
33
|
imp |
|
35 |
|
sqrt00 |
|
36 |
32 34 35
|
syl2anc |
|
37 |
36
|
bicomd |
|
38 |
37
|
necon3bid |
|
39 |
30 38
|
mpbid |
|
40 |
39
|
ex |
|
41 |
27 40
|
sylbid |
|
42 |
41
|
imp |
|
43 |
23 26 42
|
recnmulnred |
|
44 |
|
df-nel |
|
45 |
43 44
|
sylib |
|
46 |
22 45
|
eqneltrd |
|
47 |
16 46
|
eqneltrd |
|
48 |
|
df-nel |
|
49 |
47 48
|
sylibr |
|