Step |
Hyp |
Ref |
Expression |
1 |
|
oveq1 |
|
2 |
1
|
oveq2d |
|
3 |
2
|
fveq2d |
|
4 |
|
ioossre |
|
5 |
|
ax-resscn |
|
6 |
4 5
|
sstri |
|
7 |
6
|
sseli |
|
8 |
7
|
mul02d |
|
9 |
8
|
oveq2d |
|
10 |
|
ax-icn |
|
11 |
|
2cn |
|
12 |
|
picn |
|
13 |
11 12
|
mulcli |
|
14 |
10 13
|
mulcli |
|
15 |
14
|
mul01i |
|
16 |
9 15
|
eqtrdi |
|
17 |
16
|
fveq2d |
|
18 |
|
ef0 |
|
19 |
17 18
|
eqtrdi |
|
20 |
3 19
|
sylan9eq |
|
21 |
20
|
ralrimiva |
|
22 |
|
itgeq2 |
|
23 |
21 22
|
syl |
|
24 |
|
ioombl |
|
25 |
|
0re |
|
26 |
|
1re |
|
27 |
|
ioovolcl |
|
28 |
25 26 27
|
mp2an |
|
29 |
|
ax-1cn |
|
30 |
|
itgconst |
|
31 |
24 28 29 30
|
mp3an |
|
32 |
|
0le1 |
|
33 |
|
volioo |
|
34 |
25 26 32 33
|
mp3an |
|
35 |
29
|
subid1i |
|
36 |
34 35
|
eqtri |
|
37 |
36
|
oveq2i |
|
38 |
29
|
mulid1i |
|
39 |
31 37 38
|
3eqtri |
|
40 |
23 39
|
eqtrdi |
|
41 |
40
|
adantl |
|
42 |
41
|
eqcomd |
|
43 |
|
ioomax |
|
44 |
43
|
eqcomi |
|
45 |
|
0red |
|
46 |
|
1red |
|
47 |
32
|
a1i |
|
48 |
5
|
a1i |
|
49 |
48
|
sselda |
|
50 |
10
|
a1i |
|
51 |
|
2cnd |
|
52 |
12
|
a1i |
|
53 |
51 52
|
mulcld |
|
54 |
50 53
|
mulcld |
|
55 |
|
simpl |
|
56 |
55
|
zcnd |
|
57 |
54 56
|
mulcld |
|
58 |
57
|
adantr |
|
59 |
|
simpr |
|
60 |
58 59
|
mulcld |
|
61 |
60
|
efcld |
|
62 |
49 61
|
syldan |
|
63 |
57
|
adantr |
|
64 |
|
ine0 |
|
65 |
|
2ne0 |
|
66 |
|
pipos |
|
67 |
25 66
|
gtneii |
|
68 |
11 12 65 67
|
mulne0i |
|
69 |
10 13 64 68
|
mulne0i |
|
70 |
69
|
a1i |
|
71 |
|
simpr |
|
72 |
71
|
neqned |
|
73 |
54 56 70 72
|
mulne0d |
|
74 |
73
|
adantr |
|
75 |
62 63 74
|
divcld |
|
76 |
75
|
fmpttd |
|
77 |
|
reelprrecn |
|
78 |
77
|
a1i |
|
79 |
|
cnelprrecn |
|
80 |
79
|
a1i |
|
81 |
63 49
|
mulcld |
|
82 |
|
simpr |
|
83 |
82
|
efcld |
|
84 |
57
|
adantr |
|
85 |
73
|
adantr |
|
86 |
83 84 85
|
divcld |
|
87 |
26
|
a1i |
|
88 |
78
|
dvmptid |
|
89 |
78 49 87 88 57
|
dvmptcmul |
|
90 |
63
|
mulid1d |
|
91 |
90
|
mpteq2dva |
|
92 |
89 91
|
eqtrd |
|
93 |
|
dvef |
|
94 |
|
eff |
|
95 |
94
|
a1i |
|
96 |
95
|
feqmptd |
|
97 |
96
|
oveq2d |
|
98 |
93 97 96
|
3eqtr3a |
|
99 |
80 83 83 98 57 73
|
dvmptdivc |
|
100 |
|
fveq2 |
|
101 |
100
|
oveq1d |
|
102 |
78 80 81 63 86 86 92 99 101 101
|
dvmptco |
|
103 |
62 63 74
|
divcan1d |
|
104 |
103
|
mpteq2dva |
|
105 |
102 104
|
eqtrd |
|
106 |
|
efcn |
|
107 |
106
|
a1i |
|
108 |
|
resmpt |
|
109 |
5 108
|
mp1i |
|
110 |
|
eqid |
|
111 |
110
|
mulc1cncf |
|
112 |
57 111
|
syl |
|
113 |
|
rescncf |
|
114 |
5 113
|
mp1i |
|
115 |
112 114
|
mpd |
|
116 |
109 115
|
eqeltrrd |
|
117 |
107 116
|
cncfmpt1f |
|
118 |
105 117
|
eqeltrd |
|
119 |
44 45 46 47 76 118
|
ftc2re |
|
120 |
4
|
sseli |
|
121 |
105
|
adantr |
|
122 |
121
|
fveq1d |
|
123 |
|
oveq2 |
|
124 |
123
|
fveq2d |
|
125 |
124
|
cbvmptv |
|
126 |
125
|
a1i |
|
127 |
57
|
adantr |
|
128 |
48
|
sselda |
|
129 |
127 128
|
mulcld |
|
130 |
129
|
efcld |
|
131 |
126 130
|
fvmpt2d |
|
132 |
14
|
a1i |
|
133 |
56
|
adantr |
|
134 |
132 133 128
|
mulassd |
|
135 |
134
|
fveq2d |
|
136 |
131 135
|
eqtrd |
|
137 |
122 136
|
eqtrd |
|
138 |
120 137
|
sylan2 |
|
139 |
138
|
ralrimiva |
|
140 |
|
itgeq2 |
|
141 |
139 140
|
syl |
|
142 |
|
eqidd |
|
143 |
|
simpr |
|
144 |
143
|
oveq2d |
|
145 |
144
|
fveq2d |
|
146 |
145
|
oveq1d |
|
147 |
29
|
a1i |
|
148 |
57 147
|
mulcld |
|
149 |
148
|
efcld |
|
150 |
149 57 73
|
divcld |
|
151 |
142 146 46 150
|
fvmptd |
|
152 |
57
|
mulid1d |
|
153 |
152
|
fveq2d |
|
154 |
|
ef2kpi |
|
155 |
55 154
|
syl |
|
156 |
153 155
|
eqtrd |
|
157 |
156
|
oveq1d |
|
158 |
151 157
|
eqtrd |
|
159 |
|
simpr |
|
160 |
159
|
oveq2d |
|
161 |
160
|
fveq2d |
|
162 |
161
|
oveq1d |
|
163 |
5 45
|
sselid |
|
164 |
57 163
|
mulcld |
|
165 |
164
|
efcld |
|
166 |
165 57 73
|
divcld |
|
167 |
142 162 45 166
|
fvmptd |
|
168 |
57
|
mul01d |
|
169 |
168
|
fveq2d |
|
170 |
169 18
|
eqtrdi |
|
171 |
170
|
oveq1d |
|
172 |
167 171
|
eqtrd |
|
173 |
158 172
|
oveq12d |
|
174 |
157 150
|
eqeltrrd |
|
175 |
174
|
subidd |
|
176 |
173 175
|
eqtrd |
|
177 |
119 141 176
|
3eqtr3d |
|
178 |
177
|
eqcomd |
|
179 |
42 178
|
ifeqda |
|
180 |
179
|
eqcomd |
|