Step |
Hyp |
Ref |
Expression |
1 |
|
dvasin.d |
|
2 |
|
df-acos |
|
3 |
2
|
reseq1i |
|
4 |
|
difss |
|
5 |
1 4
|
eqsstri |
|
6 |
|
resmpt |
|
7 |
5 6
|
ax-mp |
|
8 |
3 7
|
eqtri |
|
9 |
8
|
oveq2i |
|
10 |
|
cnelprrecn |
|
11 |
10
|
a1i |
|
12 |
|
halfpire |
|
13 |
12
|
recni |
|
14 |
13
|
a1i |
|
15 |
|
c0ex |
|
16 |
15
|
a1i |
|
17 |
13
|
a1i |
|
18 |
15
|
a1i |
|
19 |
13
|
a1i |
|
20 |
11 19
|
dvmptc |
|
21 |
5
|
a1i |
|
22 |
|
eqid |
|
23 |
22
|
cnfldtopon |
|
24 |
23
|
toponrestid |
|
25 |
22
|
recld2 |
|
26 |
|
neg1rr |
|
27 |
|
iocmnfcld |
|
28 |
26 27
|
ax-mp |
|
29 |
22
|
tgioo2 |
|
30 |
29
|
fveq2i |
|
31 |
28 30
|
eleqtri |
|
32 |
|
restcldr |
|
33 |
25 31 32
|
mp2an |
|
34 |
|
1re |
|
35 |
|
icopnfcld |
|
36 |
34 35
|
ax-mp |
|
37 |
36 30
|
eleqtri |
|
38 |
|
restcldr |
|
39 |
25 37 38
|
mp2an |
|
40 |
|
uncld |
|
41 |
33 39 40
|
mp2an |
|
42 |
23
|
toponunii |
|
43 |
42
|
cldopn |
|
44 |
41 43
|
ax-mp |
|
45 |
1 44
|
eqeltri |
|
46 |
45
|
a1i |
|
47 |
11 17 18 20 21 24 22 46
|
dvmptres |
|
48 |
5
|
sseli |
|
49 |
|
asincl |
|
50 |
48 49
|
syl |
|
51 |
50
|
adantl |
|
52 |
|
ovexd |
|
53 |
|
asinf |
|
54 |
53
|
a1i |
|
55 |
54 21
|
feqresmpt |
|
56 |
55
|
oveq2d |
|
57 |
1
|
dvasin |
|
58 |
56 57
|
eqtr3di |
|
59 |
11 14 16 47 51 52 58
|
dvmptsub |
|
60 |
59
|
mptru |
|
61 |
|
df-neg |
|
62 |
|
1cnd |
|
63 |
|
ax-1cn |
|
64 |
48
|
sqcld |
|
65 |
|
subcl |
|
66 |
63 64 65
|
sylancr |
|
67 |
66
|
sqrtcld |
|
68 |
|
eldifn |
|
69 |
68 1
|
eleq2s |
|
70 |
|
mnfxr |
|
71 |
26
|
rexri |
|
72 |
|
mnflt |
|
73 |
26 72
|
ax-mp |
|
74 |
|
ubioc1 |
|
75 |
70 71 73 74
|
mp3an |
|
76 |
|
eleq1 |
|
77 |
75 76
|
mpbiri |
|
78 |
34
|
rexri |
|
79 |
|
pnfxr |
|
80 |
|
ltpnf |
|
81 |
34 80
|
ax-mp |
|
82 |
|
lbico1 |
|
83 |
78 79 81 82
|
mp3an |
|
84 |
|
eleq1 |
|
85 |
83 84
|
mpbiri |
|
86 |
77 85
|
orim12i |
|
87 |
86
|
orcoms |
|
88 |
|
elun |
|
89 |
87 88
|
sylibr |
|
90 |
69 89
|
nsyl |
|
91 |
|
sq1 |
|
92 |
|
1cnd |
|
93 |
|
sqcl |
|
94 |
93
|
adantr |
|
95 |
63 93 65
|
sylancr |
|
96 |
95
|
adantr |
|
97 |
|
simpr |
|
98 |
96 97
|
sqr00d |
|
99 |
92 94 98
|
subeq0d |
|
100 |
91 99
|
eqtr2id |
|
101 |
100
|
ex |
|
102 |
|
sqeqor |
|
103 |
63 102
|
mpan2 |
|
104 |
101 103
|
sylibd |
|
105 |
104
|
necon3bd |
|
106 |
48 90 105
|
sylc |
|
107 |
62 67 106
|
divnegd |
|
108 |
61 107
|
eqtr3id |
|
109 |
108
|
mpteq2ia |
|
110 |
9 60 109
|
3eqtri |
|