Step |
Hyp |
Ref |
Expression |
1 |
|
ang.1 |
|
2 |
|
ang180lem1.2 |
|
3 |
|
ang180lem1.3 |
|
4 |
|
2cn |
|
5 |
|
picn |
|
6 |
4 5
|
mulcli |
|
7 |
|
2ne0 |
|
8 |
6 4 7
|
divreci |
|
9 |
5 4 7
|
divcan3i |
|
10 |
8 9
|
eqtr3i |
|
11 |
1 2 3
|
ang180lem2 |
|
12 |
11
|
simprd |
|
13 |
|
1e0p1 |
|
14 |
12 13
|
breqtrdi |
|
15 |
1 2 3
|
ang180lem1 |
|
16 |
15
|
simpld |
|
17 |
|
0z |
|
18 |
|
zleltp1 |
|
19 |
16 17 18
|
sylancl |
|
20 |
14 19
|
mpbird |
|
21 |
20
|
adantr |
|
22 |
|
zlem1lt |
|
23 |
17 16 22
|
sylancr |
|
24 |
|
df-neg |
|
25 |
24
|
breq1i |
|
26 |
23 25
|
bitr4di |
|
27 |
26
|
biimpar |
|
28 |
16
|
zred |
|
29 |
28
|
adantr |
|
30 |
|
0re |
|
31 |
|
letri3 |
|
32 |
29 30 31
|
sylancl |
|
33 |
21 27 32
|
mpbir2and |
|
34 |
3 33
|
syl5eqr |
|
35 |
|
ax-1cn |
|
36 |
|
simp1 |
|
37 |
|
subcl |
|
38 |
35 36 37
|
sylancr |
|
39 |
|
simp3 |
|
40 |
39
|
necomd |
|
41 |
|
subeq0 |
|
42 |
35 36 41
|
sylancr |
|
43 |
42
|
necon3bid |
|
44 |
40 43
|
mpbird |
|
45 |
38 44
|
reccld |
|
46 |
38 44
|
recne0d |
|
47 |
45 46
|
logcld |
|
48 |
|
subcl |
|
49 |
36 35 48
|
sylancl |
|
50 |
|
simp2 |
|
51 |
49 36 50
|
divcld |
|
52 |
|
subeq0 |
|
53 |
36 35 52
|
sylancl |
|
54 |
53
|
necon3bid |
|
55 |
39 54
|
mpbird |
|
56 |
49 36 55 50
|
divne0d |
|
57 |
51 56
|
logcld |
|
58 |
47 57
|
addcld |
|
59 |
|
logcl |
|
60 |
59
|
3adant3 |
|
61 |
58 60
|
addcld |
|
62 |
2 61
|
eqeltrid |
|
63 |
|
ax-icn |
|
64 |
63
|
a1i |
|
65 |
|
ine0 |
|
66 |
65
|
a1i |
|
67 |
62 64 66
|
divcld |
|
68 |
6
|
a1i |
|
69 |
|
pire |
|
70 |
|
pipos |
|
71 |
69 70
|
gt0ne0ii |
|
72 |
4 5 7 71
|
mulne0i |
|
73 |
72
|
a1i |
|
74 |
67 68 73
|
divcld |
|
75 |
74
|
adantr |
|
76 |
|
halfcn |
|
77 |
|
subeq0 |
|
78 |
75 76 77
|
sylancl |
|
79 |
34 78
|
mpbid |
|
80 |
67
|
adantr |
|
81 |
6
|
a1i |
|
82 |
76
|
a1i |
|
83 |
72
|
a1i |
|
84 |
80 81 82 83
|
divmuld |
|
85 |
79 84
|
mpbid |
|
86 |
10 85
|
syl5reqr |
|
87 |
62
|
adantr |
|
88 |
63
|
a1i |
|
89 |
5
|
a1i |
|
90 |
65
|
a1i |
|
91 |
87 88 89 90
|
divmuld |
|
92 |
86 91
|
mpbid |
|
93 |
92
|
eqcomd |
|
94 |
93
|
olcd |
|
95 |
5 63
|
mulneg1i |
|
96 |
5 63
|
mulcomi |
|
97 |
96
|
negeqi |
|
98 |
95 97
|
eqtri |
|
99 |
76 6
|
mulneg1i |
|
100 |
35 4 7
|
divcan1i |
|
101 |
100
|
oveq1i |
|
102 |
76 4 5
|
mulassi |
|
103 |
5
|
mulid2i |
|
104 |
101 102 103
|
3eqtr3i |
|
105 |
104
|
negeqi |
|
106 |
99 105
|
eqtri |
|
107 |
35 76
|
negsubdii |
|
108 |
|
1mhlfehlf |
|
109 |
108
|
negeqi |
|
110 |
107 109
|
eqtr3i |
|
111 |
|
simpr |
|
112 |
111 3
|
eqtrdi |
|
113 |
112
|
oveq1d |
|
114 |
110 113
|
syl5eqr |
|
115 |
|
npcan |
|
116 |
74 76 115
|
sylancl |
|
117 |
116
|
adantr |
|
118 |
114 117
|
eqtrd |
|
119 |
118
|
oveq1d |
|
120 |
106 119
|
syl5eqr |
|
121 |
67 68 73
|
divcan1d |
|
122 |
121
|
adantr |
|
123 |
120 122
|
eqtrd |
|
124 |
123
|
oveq1d |
|
125 |
98 124
|
syl5eqr |
|
126 |
62 64 66
|
divcan1d |
|
127 |
126
|
adantr |
|
128 |
125 127
|
eqtr2d |
|
129 |
128
|
orcd |
|
130 |
|
df-2 |
|
131 |
130
|
negeqi |
|
132 |
|
negdi2 |
|
133 |
35 35 132
|
mp2an |
|
134 |
131 133
|
eqtri |
|
135 |
11
|
simpld |
|
136 |
134 135
|
eqbrtrrid |
|
137 |
|
neg1z |
|
138 |
|
zlem1lt |
|
139 |
137 16 138
|
sylancr |
|
140 |
136 139
|
mpbird |
|
141 |
|
neg1rr |
|
142 |
|
leloe |
|
143 |
141 28 142
|
sylancr |
|
144 |
140 143
|
mpbid |
|
145 |
94 129 144
|
mpjaodan |
|
146 |
2
|
ovexi |
|
147 |
146
|
elpr |
|
148 |
145 147
|
sylibr |
|