Step |
Hyp |
Ref |
Expression |
1 |
|
2sphere.i |
|
2 |
|
2sphere.e |
|
3 |
|
2sphere.p |
|
4 |
|
2sphere.s |
|
5 |
|
2sphere0.0 |
|
6 |
|
2sphere0.c |
|
7 |
|
prex |
|
8 |
1 7
|
eqeltri |
|
9 |
5 3
|
rrx0el |
|
10 |
8 9
|
ax-mp |
|
11 |
|
eqid |
|
12 |
1 2 3 4 11
|
2sphere |
|
13 |
10 12
|
mpan |
|
14 |
5
|
fveq1i |
|
15 |
|
c0ex |
|
16 |
|
1ex |
|
17 |
16
|
prid1 |
|
18 |
17 1
|
eleqtrri |
|
19 |
|
fvconst2g |
|
20 |
15 18 19
|
mp2an |
|
21 |
14 20
|
eqtri |
|
22 |
21
|
a1i |
|
23 |
22
|
oveq2d |
|
24 |
1 3
|
rrx2pxel |
|
25 |
24
|
recnd |
|
26 |
25
|
subid1d |
|
27 |
23 26
|
eqtrd |
|
28 |
27
|
oveq1d |
|
29 |
5
|
fveq1i |
|
30 |
|
2ex |
|
31 |
30
|
prid2 |
|
32 |
31 1
|
eleqtrri |
|
33 |
|
fvconst2g |
|
34 |
15 32 33
|
mp2an |
|
35 |
29 34
|
eqtri |
|
36 |
35
|
a1i |
|
37 |
36
|
oveq2d |
|
38 |
1 3
|
rrx2pyel |
|
39 |
38
|
recnd |
|
40 |
39
|
subid1d |
|
41 |
37 40
|
eqtrd |
|
42 |
41
|
oveq1d |
|
43 |
28 42
|
oveq12d |
|
44 |
43
|
eqeq1d |
|
45 |
44
|
adantl |
|
46 |
45
|
rabbidva |
|
47 |
46 6
|
eqtr4di |
|
48 |
13 47
|
eqtrd |
|