Step |
Hyp |
Ref |
Expression |
1 |
|
2sphere.i |
|
2 |
|
2sphere.e |
|
3 |
|
2sphere.p |
|
4 |
|
2sphere.s |
|
5 |
|
2sphere.c |
|
6 |
|
prfi |
|
7 |
1 6
|
eqeltri |
|
8 |
|
simpl |
|
9 |
|
elrege0 |
|
10 |
9
|
simplbi |
|
11 |
10
|
adantl |
|
12 |
|
eqid |
|
13 |
2 3 12 4
|
rrxsphere |
|
14 |
7 8 11 13
|
mp3an2i |
|
15 |
9
|
biimpi |
|
16 |
15
|
ad2antlr |
|
17 |
|
sqrtsq |
|
18 |
16 17
|
syl |
|
19 |
18
|
eqeq2d |
|
20 |
1 3
|
rrx2pxel |
|
21 |
20
|
adantl |
|
22 |
1 3
|
rrx2pxel |
|
23 |
22
|
adantr |
|
24 |
21 23
|
resubcld |
|
25 |
24
|
resqcld |
|
26 |
1 3
|
rrx2pyel |
|
27 |
26
|
adantl |
|
28 |
1 3
|
rrx2pyel |
|
29 |
28
|
adantr |
|
30 |
27 29
|
resubcld |
|
31 |
30
|
resqcld |
|
32 |
25 31
|
readdcld |
|
33 |
24
|
sqge0d |
|
34 |
30
|
sqge0d |
|
35 |
25 31 33 34
|
addge0d |
|
36 |
32 35
|
jca |
|
37 |
36
|
adantlr |
|
38 |
|
resqcl |
|
39 |
|
sqge0 |
|
40 |
38 39
|
jca |
|
41 |
10 40
|
syl |
|
42 |
41
|
ad2antlr |
|
43 |
|
sqrt11 |
|
44 |
37 42 43
|
syl2anc |
|
45 |
8
|
anim1ci |
|
46 |
|
2nn0 |
|
47 |
|
eqid |
|
48 |
47
|
ehlval |
|
49 |
46 48
|
ax-mp |
|
50 |
|
fz12pr |
|
51 |
50 1
|
eqtr4i |
|
52 |
51
|
fveq2i |
|
53 |
49 52
|
eqtri |
|
54 |
2 53
|
eqtr4i |
|
55 |
1
|
oveq2i |
|
56 |
3 55
|
eqtri |
|
57 |
54 56 12
|
ehl2eudisval |
|
58 |
45 57
|
syl |
|
59 |
58
|
eqcomd |
|
60 |
59
|
eqeq1d |
|
61 |
19 44 60
|
3bitr3d |
|
62 |
61
|
rabbidva |
|
63 |
5 62
|
syl5req |
|
64 |
14 63
|
eqtrd |
|