Step |
Hyp |
Ref |
Expression |
1 |
|
0cn |
|
2 |
|
sqrtval |
|
3 |
1 2
|
ax-mp |
|
4 |
|
id |
|
5 |
|
sqeq0 |
|
6 |
5
|
biimpa |
|
7 |
6
|
3ad2antr1 |
|
8 |
7
|
ex |
|
9 |
|
sq0i |
|
10 |
|
0le0 |
|
11 |
|
fveq2 |
|
12 |
|
re0 |
|
13 |
11 12
|
eqtrdi |
|
14 |
10 13
|
breqtrrid |
|
15 |
|
0re |
|
16 |
|
eleq1 |
|
17 |
15 16
|
mpbiri |
|
18 |
|
rennim |
|
19 |
17 18
|
syl |
|
20 |
9 14 19
|
3jca |
|
21 |
8 20
|
impbid1 |
|
22 |
21
|
adantl |
|
23 |
4 22
|
riota5 |
|
24 |
1 23
|
ax-mp |
|
25 |
3 24
|
eqtri |
|