Step |
Hyp |
Ref |
Expression |
1 |
|
log2cnv.1 |
|
2 |
|
nn0uz |
|
3 |
|
0zd |
|
4 |
|
2cn |
|
5 |
|
ax-icn |
|
6 |
|
ine0 |
|
7 |
4 5 6
|
divcli |
|
8 |
7
|
a1i |
|
9 |
|
3cn |
|
10 |
|
3ne0 |
|
11 |
5 9 10
|
divcli |
|
12 |
|
absdiv |
|
13 |
5 9 10 12
|
mp3an |
|
14 |
|
absi |
|
15 |
|
3re |
|
16 |
|
0re |
|
17 |
|
3pos |
|
18 |
16 15 17
|
ltleii |
|
19 |
|
absid |
|
20 |
15 18 19
|
mp2an |
|
21 |
14 20
|
oveq12i |
|
22 |
13 21
|
eqtri |
|
23 |
|
1lt3 |
|
24 |
|
recgt1 |
|
25 |
15 17 24
|
mp2an |
|
26 |
23 25
|
mpbi |
|
27 |
22 26
|
eqbrtri |
|
28 |
|
eqid |
|
29 |
28
|
atantayl3 |
|
30 |
11 27 29
|
mp2an |
|
31 |
30
|
a1i |
|
32 |
|
oveq2 |
|
33 |
|
oveq2 |
|
34 |
33
|
oveq1d |
|
35 |
34
|
oveq2d |
|
36 |
35 34
|
oveq12d |
|
37 |
32 36
|
oveq12d |
|
38 |
|
ovex |
|
39 |
37 28 38
|
fvmpt |
|
40 |
5
|
a1i |
|
41 |
9
|
a1i |
|
42 |
10
|
a1i |
|
43 |
|
2nn0 |
|
44 |
|
nn0mulcl |
|
45 |
43 44
|
mpan |
|
46 |
|
peano2nn0 |
|
47 |
45 46
|
syl |
|
48 |
40 41 42 47
|
expdivd |
|
49 |
48
|
oveq2d |
|
50 |
|
neg1cn |
|
51 |
|
expcl |
|
52 |
50 51
|
mpan |
|
53 |
|
expcl |
|
54 |
5 47 53
|
sylancr |
|
55 |
|
3nn |
|
56 |
|
nnexpcl |
|
57 |
55 47 56
|
sylancr |
|
58 |
57
|
nncnd |
|
59 |
57
|
nnne0d |
|
60 |
52 54 58 59
|
divassd |
|
61 |
|
expp1 |
|
62 |
5 45 61
|
sylancr |
|
63 |
|
expmul |
|
64 |
5 43 63
|
mp3an12 |
|
65 |
|
i2 |
|
66 |
65
|
oveq1i |
|
67 |
64 66
|
eqtrdi |
|
68 |
67
|
oveq1d |
|
69 |
62 68
|
eqtrd |
|
70 |
69
|
oveq2d |
|
71 |
52 52 40
|
mulassd |
|
72 |
50
|
a1i |
|
73 |
|
id |
|
74 |
72 73 73
|
expaddd |
|
75 |
|
expmul |
|
76 |
50 43 75
|
mp3an12 |
|
77 |
|
neg1sqe1 |
|
78 |
77
|
oveq1i |
|
79 |
76 78
|
eqtrdi |
|
80 |
|
nn0cn |
|
81 |
80
|
2timesd |
|
82 |
81
|
oveq2d |
|
83 |
|
nn0z |
|
84 |
|
1exp |
|
85 |
83 84
|
syl |
|
86 |
79 82 85
|
3eqtr3d |
|
87 |
74 86
|
eqtr3d |
|
88 |
87
|
oveq1d |
|
89 |
5
|
mulid2i |
|
90 |
88 89
|
eqtrdi |
|
91 |
70 71 90
|
3eqtr2d |
|
92 |
91
|
oveq1d |
|
93 |
49 60 92
|
3eqtr2d |
|
94 |
93
|
oveq1d |
|
95 |
|
expcl |
|
96 |
11 47 95
|
sylancr |
|
97 |
|
nn0p1nn |
|
98 |
45 97
|
syl |
|
99 |
98
|
nncnd |
|
100 |
98
|
nnne0d |
|
101 |
52 96 99 100
|
divassd |
|
102 |
40 58 99 59 100
|
divdiv1d |
|
103 |
94 101 102
|
3eqtr3d |
|
104 |
58 99
|
mulcomd |
|
105 |
104
|
oveq2d |
|
106 |
39 103 105
|
3eqtrd |
|
107 |
98 57
|
nnmulcld |
|
108 |
107
|
nncnd |
|
109 |
107
|
nnne0d |
|
110 |
40 108 109
|
divcld |
|
111 |
106 110
|
eqeltrd |
|
112 |
111
|
adantl |
|
113 |
34
|
oveq2d |
|
114 |
|
oveq2 |
|
115 |
113 114
|
oveq12d |
|
116 |
115
|
oveq2d |
|
117 |
|
ovex |
|
118 |
116 1 117
|
fvmpt |
|
119 |
|
expp1 |
|
120 |
9 45 119
|
sylancr |
|
121 |
|
expmul |
|
122 |
9 43 121
|
mp3an12 |
|
123 |
|
sq3 |
|
124 |
123
|
oveq1i |
|
125 |
122 124
|
eqtrdi |
|
126 |
125
|
oveq1d |
|
127 |
|
9nn |
|
128 |
|
nnexpcl |
|
129 |
127 128
|
mpan |
|
130 |
129
|
nncnd |
|
131 |
|
mulcom |
|
132 |
130 9 131
|
sylancl |
|
133 |
120 126 132
|
3eqtrd |
|
134 |
91 133
|
oveq12d |
|
135 |
49 60 134
|
3eqtr2d |
|
136 |
135
|
oveq1d |
|
137 |
|
nnmulcl |
|
138 |
55 129 137
|
sylancr |
|
139 |
138
|
nncnd |
|
140 |
138
|
nnne0d |
|
141 |
40 139 99 140 100
|
divdiv1d |
|
142 |
136 101 141
|
3eqtr3d |
|
143 |
41 130 99
|
mul32d |
|
144 |
143
|
oveq2d |
|
145 |
39 142 144
|
3eqtrd |
|
146 |
145
|
oveq2d |
|
147 |
|
nnmulcl |
|
148 |
55 98 147
|
sylancr |
|
149 |
148 129
|
nnmulcld |
|
150 |
149
|
nncnd |
|
151 |
149
|
nnne0d |
|
152 |
40 150 151
|
divcld |
|
153 |
|
mulcom |
|
154 |
152 7 153
|
sylancl |
|
155 |
4
|
a1i |
|
156 |
6
|
a1i |
|
157 |
155 40 150 156 151
|
dmdcand |
|
158 |
146 154 157
|
3eqtr2d |
|
159 |
118 158
|
eqtr4d |
|
160 |
159
|
adantl |
|
161 |
2 3 8 31 112 160
|
isermulc2 |
|
162 |
161
|
mptru |
|
163 |
|
bndatandm |
|
164 |
11 27 163
|
mp2an |
|
165 |
|
atanval |
|
166 |
164 165
|
ax-mp |
|
167 |
|
df-4 |
|
168 |
167
|
oveq1i |
|
169 |
|
ax-1cn |
|
170 |
9 169 9 10
|
divdiri |
|
171 |
9 10
|
dividi |
|
172 |
171
|
oveq1i |
|
173 |
168 170 172
|
3eqtri |
|
174 |
169 9 10
|
divcli |
|
175 |
169 174
|
subnegi |
|
176 |
|
divneg |
|
177 |
169 9 10 176
|
mp3an |
|
178 |
|
ixi |
|
179 |
178
|
oveq1i |
|
180 |
5 5 9 10
|
divassi |
|
181 |
177 179 180
|
3eqtr2i |
|
182 |
181
|
oveq2i |
|
183 |
173 175 182
|
3eqtr2ri |
|
184 |
183
|
fveq2i |
|
185 |
9 10
|
pm3.2i |
|
186 |
|
divsubdir |
|
187 |
9 169 185 186
|
mp3an |
|
188 |
|
3m1e2 |
|
189 |
188
|
oveq1i |
|
190 |
171
|
oveq1i |
|
191 |
187 189 190
|
3eqtr3i |
|
192 |
169 174
|
negsubi |
|
193 |
181
|
oveq2i |
|
194 |
191 192 193
|
3eqtr2ri |
|
195 |
194
|
fveq2i |
|
196 |
184 195
|
oveq12i |
|
197 |
|
4re |
|
198 |
|
4pos |
|
199 |
197 198
|
elrpii |
|
200 |
|
3rp |
|
201 |
|
rpdivcl |
|
202 |
199 200 201
|
mp2an |
|
203 |
|
2rp |
|
204 |
|
rpdivcl |
|
205 |
203 200 204
|
mp2an |
|
206 |
|
relogdiv |
|
207 |
202 205 206
|
mp2an |
|
208 |
|
4cn |
|
209 |
|
2cnne0 |
|
210 |
|
divcan7 |
|
211 |
208 209 185 210
|
mp3an |
|
212 |
|
4d2e2 |
|
213 |
211 212
|
eqtri |
|
214 |
213
|
fveq2i |
|
215 |
196 207 214
|
3eqtr2i |
|
216 |
215
|
oveq2i |
|
217 |
166 216
|
eqtri |
|
218 |
217
|
oveq2i |
|
219 |
|
2ne0 |
|
220 |
5 4 219
|
divcli |
|
221 |
|
logcl |
|
222 |
4 219 221
|
mp2an |
|
223 |
7 220 222
|
mulassi |
|
224 |
218 223
|
eqtr4i |
|
225 |
|
divcan6 |
|
226 |
4 219 5 6 225
|
mp4an |
|
227 |
226
|
oveq1i |
|
228 |
222
|
mulid2i |
|
229 |
224 227 228
|
3eqtri |
|
230 |
162 229
|
breqtri |
|