Step |
Hyp |
Ref |
Expression |
1 |
|
pire |
|
2 |
|
pipos |
|
3 |
1 2
|
elrpii |
|
4 |
|
2ne0 |
|
5 |
4
|
a1i |
|
6 |
|
2cn |
|
7 |
|
2re |
|
8 |
7
|
a1i |
|
9 |
6 8
|
ax-mp |
|
10 |
9
|
a1i |
|
11 |
|
id |
|
12 |
11
|
adantr |
|
13 |
6
|
a1i |
|
14 |
13 11
|
mulcld |
|
15 |
|
ax-icn |
|
16 |
15
|
a1i |
|
17 |
13 16 11
|
mul12d |
|
18 |
16 11
|
mulcld |
|
19 |
18
|
2timesd |
|
20 |
17 19
|
eqtr3d |
|
21 |
20
|
fveq2d |
|
22 |
|
efadd |
|
23 |
18 18 22
|
syl2anc |
|
24 |
21 23
|
eqtrd |
|
25 |
24
|
adantr |
|
26 |
|
sinval |
|
27 |
|
id |
|
28 |
26 27
|
sylan9req |
|
29 |
|
efcl |
|
30 |
18 29
|
syl |
|
31 |
|
negicn |
|
32 |
31
|
a1i |
|
33 |
32 11
|
mulcld |
|
34 |
|
efcl |
|
35 |
33 34
|
syl |
|
36 |
30 35
|
subcld |
|
37 |
|
2mulicn |
|
38 |
37
|
a1i |
|
39 |
|
2muline0 |
|
40 |
39
|
a1i |
|
41 |
36 38 40
|
diveq0ad |
|
42 |
41
|
adantr |
|
43 |
28 42
|
mpbid |
|
44 |
30 35
|
subeq0ad |
|
45 |
44
|
adantr |
|
46 |
43 45
|
mpbid |
|
47 |
46
|
oveq2d |
|
48 |
|
efadd |
|
49 |
18 33 48
|
syl2anc |
|
50 |
49
|
adantr |
|
51 |
47 50
|
eqtr4d |
|
52 |
15
|
negidi |
|
53 |
52
|
oveq1i |
|
54 |
16 32 11
|
adddird |
|
55 |
53 54
|
syl5reqr |
|
56 |
11
|
mul02d |
|
57 |
55 56
|
eqtrd |
|
58 |
57
|
fveq2d |
|
59 |
58
|
adantr |
|
60 |
|
ef0 |
|
61 |
60
|
a1i |
|
62 |
51 59 61
|
3eqtrd |
|
63 |
25 62
|
eqtrd |
|
64 |
63
|
fveq2d |
|
65 |
|
abs1 |
|
66 |
64 65
|
eqtrdi |
|
67 |
|
absefib |
|
68 |
67
|
biimparc |
|
69 |
68
|
ancoms |
|
70 |
14 66 69
|
syl2an2r |
|
71 |
|
mulre |
|
72 |
71
|
4animp1 |
|
73 |
72
|
4an31 |
|
74 |
5 10 12 70 73
|
syl1111anc |
|
75 |
3
|
a1i |
|
76 |
74 75
|
modcld |
|
77 |
76
|
recnd |
|
78 |
77
|
sincld |
|
79 |
1
|
a1i |
|
80 |
|
0re |
|
81 |
80 1 2
|
ltleii |
|
82 |
|
gt0ne0 |
|
83 |
82
|
3adant3 |
|
84 |
83
|
3com23 |
|
85 |
1 81 2 84
|
mp3an |
|
86 |
85
|
a1i |
|
87 |
74 79 86
|
redivcld |
|
88 |
87
|
flcld |
|
89 |
88
|
znegcld |
|
90 |
|
abssinper |
|
91 |
90
|
eqcomd |
|
92 |
91
|
ex |
|
93 |
92
|
adantr |
|
94 |
89 93
|
mpd |
|
95 |
88
|
zcnd |
|
96 |
95
|
negcld |
|
97 |
1
|
recni |
|
98 |
97
|
a1i |
|
99 |
96 98
|
mulcld |
|
100 |
98 95
|
mulcld |
|
101 |
100
|
negcld |
|
102 |
95 98
|
mulneg1d |
|
103 |
95 98
|
mulcomd |
|
104 |
103
|
negeqd |
|
105 |
102 104
|
eqtrd |
|
106 |
|
oveq2 |
|
107 |
106
|
ad3antrrr |
|
108 |
107
|
4an4132 |
|
109 |
12 99 101 105 108
|
syl1111anc |
|
110 |
12 100
|
negsubd |
|
111 |
109 110
|
eqtrd |
|
112 |
111
|
fveq2d |
|
113 |
112
|
fveq2d |
|
114 |
94 113
|
eqtrd |
|
115 |
|
modval |
|
116 |
115
|
fveq2d |
|
117 |
116
|
fveq2d |
|
118 |
3 117
|
mpan2 |
|
119 |
74 118
|
syl |
|
120 |
114 119
|
eqtr4d |
|
121 |
27
|
fveq2d |
|
122 |
|
abs0 |
|
123 |
121 122
|
eqtrdi |
|
124 |
123
|
adantl |
|
125 |
120 124
|
eqtr3d |
|
126 |
78 125
|
abs00d |
|
127 |
|
notnotb |
|
128 |
127
|
bicomi |
|
129 |
|
ltne |
|
130 |
129
|
neneqd |
|
131 |
130
|
expcom |
|
132 |
80 131
|
mpi |
|
133 |
132
|
con3i |
|
134 |
128 133
|
sylbir |
|
135 |
126 134
|
syl |
|
136 |
|
sinq12gt0 |
|
137 |
135 136
|
nsyl |
|
138 |
80
|
rexri |
|
139 |
1
|
rexri |
|
140 |
|
elioo2 |
|
141 |
138 139 140
|
mp2an |
|
142 |
141
|
notbii |
|
143 |
137 142
|
sylib |
|
144 |
|
3anan12 |
|
145 |
144
|
notbii |
|
146 |
143 145
|
sylib |
|
147 |
|
modlt |
|
148 |
147
|
ancoms |
|
149 |
3 74 148
|
sylancr |
|
150 |
76 149
|
jca |
|
151 |
|
not12an2impnot1 |
|
152 |
146 150 151
|
syl2anc |
|
153 |
|
modge0 |
|
154 |
153
|
ancoms |
|
155 |
3 74 154
|
sylancr |
|
156 |
|
leloe |
|
157 |
156
|
biimp3a |
|
158 |
157
|
idiALT |
|
159 |
80 76 155 158
|
mp3an2i |
|
160 |
|
pm2.53 |
|
161 |
160
|
imp |
|
162 |
161
|
ancoms |
|
163 |
152 159 162
|
syl2anc |
|
164 |
163
|
eqcomd |
|
165 |
|
mod0 |
|
166 |
165
|
biimp3a |
|
167 |
166
|
3com12 |
|
168 |
3 74 164 167
|
mp3an2i |
|
169 |
168
|
ex |
|
170 |
97
|
a1i |
|
171 |
85
|
a1i |
|
172 |
11 170 171
|
divcan1d |
|
173 |
172
|
fveq2d |
|
174 |
|
id |
|
175 |
|
sinkpi |
|
176 |
174 175
|
syl |
|
177 |
173 176
|
sylan9req |
|
178 |
177
|
ex |
|
179 |
169 178
|
impbid |
|