Step |
Hyp |
Ref |
Expression |
1 |
|
fveq2 |
|
2 |
|
re0 |
|
3 |
1 2
|
eqtrdi |
|
4 |
3
|
necon3i |
|
5 |
|
logcl |
|
6 |
4 5
|
sylan2 |
|
7 |
6
|
imcld |
|
8 |
7
|
recnd |
|
9 |
|
sqcl |
|
10 |
9
|
adantr |
|
11 |
|
abscl |
|
12 |
11
|
adantr |
|
13 |
12
|
recnd |
|
14 |
13
|
sqcld |
|
15 |
|
absrpcl |
|
16 |
4 15
|
sylan2 |
|
17 |
16
|
rpne0d |
|
18 |
|
sqne0 |
|
19 |
13 18
|
syl |
|
20 |
17 19
|
mpbird |
|
21 |
10 14 14 20
|
divdird |
|
22 |
|
ax-icn |
|
23 |
|
mulcl |
|
24 |
22 8 23
|
sylancr |
|
25 |
|
2z |
|
26 |
|
efexp |
|
27 |
24 25 26
|
sylancl |
|
28 |
|
efiarg |
|
29 |
4 28
|
sylan2 |
|
30 |
29
|
oveq1d |
|
31 |
|
simpl |
|
32 |
31 13 17
|
sqdivd |
|
33 |
27 30 32
|
3eqtrrd |
|
34 |
14 20
|
dividd |
|
35 |
33 34
|
oveq12d |
|
36 |
21 35
|
eqtr2d |
|
37 |
10 14
|
addcld |
|
38 |
22
|
a1i |
|
39 |
|
2cn |
|
40 |
|
recl |
|
41 |
40
|
adantr |
|
42 |
41
|
recnd |
|
43 |
42
|
sqcld |
|
44 |
|
mulcl |
|
45 |
39 43 44
|
sylancr |
|
46 |
39
|
a1i |
|
47 |
|
imcl |
|
48 |
47
|
adantr |
|
49 |
48
|
recnd |
|
50 |
42 49
|
mulcld |
|
51 |
38 46 50
|
mul12d |
|
52 |
38 42 49
|
mul12d |
|
53 |
52
|
oveq2d |
|
54 |
51 53
|
eqtrd |
|
55 |
|
mulcl |
|
56 |
22 49 55
|
sylancr |
|
57 |
42 56
|
mulcld |
|
58 |
|
mulcl |
|
59 |
39 57 58
|
sylancr |
|
60 |
54 59
|
eqeltrd |
|
61 |
38 45 60
|
adddid |
|
62 |
|
mulcl |
|
63 |
42 22 62
|
sylancl |
|
64 |
46 63 42
|
mulassd |
|
65 |
42
|
sqvald |
|
66 |
65
|
oveq1d |
|
67 |
|
mulcom |
|
68 |
43 22 67
|
sylancl |
|
69 |
42 42 38
|
mul32d |
|
70 |
66 68 69
|
3eqtr3d |
|
71 |
70
|
oveq2d |
|
72 |
46 38 43
|
mul12d |
|
73 |
64 71 72
|
3eqtr2d |
|
74 |
|
ixi |
|
75 |
74
|
oveq1i |
|
76 |
|
mulcl |
|
77 |
39 49 76
|
sylancr |
|
78 |
77 42
|
mulcld |
|
79 |
38 38 78
|
mulassd |
|
80 |
75 79
|
syl5eqr |
|
81 |
78
|
mulm1d |
|
82 |
46 49 42
|
mulassd |
|
83 |
49 42
|
mulcomd |
|
84 |
83
|
oveq2d |
|
85 |
82 84
|
eqtrd |
|
86 |
85
|
oveq2d |
|
87 |
86
|
oveq2d |
|
88 |
80 81 87
|
3eqtr3d |
|
89 |
73 88
|
oveq12d |
|
90 |
|
mulcl |
|
91 |
39 63 90
|
sylancr |
|
92 |
91 42
|
mulcld |
|
93 |
92 78
|
negsubd |
|
94 |
61 89 93
|
3eqtr2d |
|
95 |
49
|
sqcld |
|
96 |
59 95
|
subcld |
|
97 |
43 96 43 95
|
add4d |
|
98 |
|
replim |
|
99 |
98
|
adantr |
|
100 |
99
|
oveq1d |
|
101 |
|
binom2 |
|
102 |
42 56 101
|
syl2anc |
|
103 |
|
sqmul |
|
104 |
22 49 103
|
sylancr |
|
105 |
|
i2 |
|
106 |
105
|
oveq1i |
|
107 |
104 106
|
eqtrdi |
|
108 |
95
|
mulm1d |
|
109 |
107 108
|
eqtrd |
|
110 |
109
|
oveq2d |
|
111 |
43 59
|
addcld |
|
112 |
111 95
|
negsubd |
|
113 |
102 110 112
|
3eqtrd |
|
114 |
43 59 95
|
addsubassd |
|
115 |
100 113 114
|
3eqtrd |
|
116 |
|
absvalsq2 |
|
117 |
116
|
adantr |
|
118 |
115 117
|
oveq12d |
|
119 |
43
|
2timesd |
|
120 |
59 95
|
npcand |
|
121 |
53 51 120
|
3eqtr4d |
|
122 |
119 121
|
oveq12d |
|
123 |
97 118 122
|
3eqtr4d |
|
124 |
123
|
oveq2d |
|
125 |
91 77 42
|
subdird |
|
126 |
94 124 125
|
3eqtr4d |
|
127 |
91 77
|
subcld |
|
128 |
|
mulcom |
|
129 |
42 22 128
|
sylancl |
|
130 |
|
simpr |
|
131 |
|
eleq1 |
|
132 |
48 131
|
syl5ibrcom |
|
133 |
|
rimul |
|
134 |
41 132 133
|
syl6an |
|
135 |
134
|
necon3d |
|
136 |
130 135
|
mpd |
|
137 |
129 136
|
eqnetrd |
|
138 |
91 77
|
subeq0ad |
|
139 |
|
2ne0 |
|
140 |
139
|
a1i |
|
141 |
63 49 46 140
|
mulcand |
|
142 |
138 141
|
bitrd |
|
143 |
142
|
necon3bid |
|
144 |
137 143
|
mpbird |
|
145 |
127 42 144 130
|
mulne0d |
|
146 |
126 145
|
eqnetrd |
|
147 |
|
oveq2 |
|
148 |
|
it0e0 |
|
149 |
147 148
|
eqtrdi |
|
150 |
149
|
necon3i |
|
151 |
146 150
|
syl |
|
152 |
37 14 151 20
|
divne0d |
|
153 |
36 152
|
eqnetrd |
|
154 |
|
tanval3 |
|
155 |
8 153 154
|
syl2anc |
|
156 |
10 14 14 20
|
divsubdird |
|
157 |
33 34
|
oveq12d |
|
158 |
156 157
|
eqtr2d |
|
159 |
36
|
oveq2d |
|
160 |
38 37 14 20
|
divassd |
|
161 |
159 160
|
eqtr4d |
|
162 |
158 161
|
oveq12d |
|
163 |
10 14
|
subcld |
|
164 |
|
mulcl |
|
165 |
22 37 164
|
sylancr |
|
166 |
163 165 14 146 20
|
divcan7d |
|
167 |
115 117
|
oveq12d |
|
168 |
43 96 95
|
pnpcand |
|
169 |
59 95 95
|
subsub4d |
|
170 |
95
|
2timesd |
|
171 |
170
|
oveq2d |
|
172 |
46 63 49
|
mulassd |
|
173 |
42 38 49
|
mulassd |
|
174 |
173
|
oveq2d |
|
175 |
172 174
|
eqtr2d |
|
176 |
49
|
sqvald |
|
177 |
176
|
oveq2d |
|
178 |
46 49 49
|
mulassd |
|
179 |
177 178
|
eqtr4d |
|
180 |
175 179
|
oveq12d |
|
181 |
91 77 49
|
subdird |
|
182 |
180 181
|
eqtr4d |
|
183 |
169 171 182
|
3eqtr2d |
|
184 |
167 168 183
|
3eqtrd |
|
185 |
184 126
|
oveq12d |
|
186 |
49 42 127 130 144
|
divcan5d |
|
187 |
166 185 186
|
3eqtrd |
|
188 |
155 162 187
|
3eqtrd |
|