Step |
Hyp |
Ref |
Expression |
1 |
|
spheres.b |
|
2 |
|
spheres.l |
|
3 |
|
spheres.d |
|
4 |
2
|
a1i |
|
5 |
|
df-sph |
|
6 |
|
fveq2 |
|
7 |
1
|
eqcomi |
|
8 |
7
|
a1i |
|
9 |
6 8
|
eqtrd |
|
10 |
|
eqidd |
|
11 |
|
fveq2 |
|
12 |
3
|
eqcomi |
|
13 |
12
|
a1i |
|
14 |
11 13
|
eqtrd |
|
15 |
14
|
oveqd |
|
16 |
15
|
eqeq1d |
|
17 |
9 16
|
rabeqbidv |
|
18 |
9 10 17
|
mpoeq123dv |
|
19 |
|
elex |
|
20 |
|
fvex |
|
21 |
1 20
|
eqeltri |
|
22 |
|
ovex |
|
23 |
21 22
|
mpoex |
|
24 |
23
|
a1i |
|
25 |
5 18 19 24
|
fvmptd3 |
|
26 |
4 25
|
eqtrd |
|