Step |
Hyp |
Ref |
Expression |
1 |
|
norm3dif.1 |
|
2 |
|
norm3dif.2 |
|
3 |
|
norm3dif.3 |
|
4 |
1 2
|
hvsubvali |
|
5 |
1 3
|
hvsubvali |
|
6 |
3 2
|
hvsubvali |
|
7 |
5 6
|
oveq12i |
|
8 |
|
neg1cn |
|
9 |
8 3
|
hvmulcli |
|
10 |
8 2
|
hvmulcli |
|
11 |
3 10
|
hvaddcli |
|
12 |
1 9 11
|
hvassi |
|
13 |
9 3 10
|
hvassi |
|
14 |
9 3
|
hvcomi |
|
15 |
3 3
|
hvsubvali |
|
16 |
|
hvsubid |
|
17 |
3 16
|
ax-mp |
|
18 |
14 15 17
|
3eqtr2i |
|
19 |
18
|
oveq1i |
|
20 |
|
ax-hv0cl |
|
21 |
20 10
|
hvcomi |
|
22 |
|
ax-hvaddid |
|
23 |
10 22
|
ax-mp |
|
24 |
19 21 23
|
3eqtri |
|
25 |
13 24
|
eqtr3i |
|
26 |
25
|
oveq2i |
|
27 |
7 12 26
|
3eqtri |
|
28 |
4 27
|
eqtr4i |
|
29 |
28
|
fveq2i |
|
30 |
1 3
|
hvsubcli |
|
31 |
3 2
|
hvsubcli |
|
32 |
30 31
|
norm-ii-i |
|
33 |
29 32
|
eqbrtri |
|