Step |
Hyp |
Ref |
Expression |
1 |
|
ftc2nc.a |
|
2 |
|
ftc2nc.b |
|
3 |
|
ftc2nc.le |
|
4 |
|
ftc2nc.c |
|
5 |
|
ftc2nc.i |
|
6 |
|
ftc2nc.f |
|
7 |
1
|
rexrd |
|
8 |
2
|
rexrd |
|
9 |
|
ubicc2 |
|
10 |
7 8 3 9
|
syl3anc |
|
11 |
|
fvex |
|
12 |
11
|
fvconst2 |
|
13 |
10 12
|
syl |
|
14 |
|
eqid |
|
15 |
14
|
subcn |
|
16 |
15
|
a1i |
|
17 |
|
eqid |
|
18 |
|
ssidd |
|
19 |
|
ioossre |
|
20 |
19
|
a1i |
|
21 |
|
cncff |
|
22 |
4 21
|
syl |
|
23 |
|
ioof |
|
24 |
|
ffun |
|
25 |
23 24
|
ax-mp |
|
26 |
|
fvelima |
|
27 |
25 26
|
mpan |
|
28 |
|
1st2nd2 |
|
29 |
28
|
fveq2d |
|
30 |
|
df-ov |
|
31 |
29 30
|
eqtr4di |
|
32 |
31
|
eqeq1d |
|
33 |
32
|
adantl |
|
34 |
7 8
|
jca |
|
35 |
34
|
adantr |
|
36 |
|
xp1st |
|
37 |
|
elicc1 |
|
38 |
7 8 37
|
syl2anc |
|
39 |
38
|
biimpa |
|
40 |
39
|
simp2d |
|
41 |
36 40
|
sylan2 |
|
42 |
|
xp2nd |
|
43 |
|
iccleub |
|
44 |
43
|
3expa |
|
45 |
34 42 44
|
syl2an |
|
46 |
|
ioossioo |
|
47 |
35 41 45 46
|
syl12anc |
|
48 |
47
|
sselda |
|
49 |
22
|
ffvelrnda |
|
50 |
49
|
adantlr |
|
51 |
48 50
|
syldan |
|
52 |
|
ioombl |
|
53 |
52
|
a1i |
|
54 |
|
fvexd |
|
55 |
22
|
feqmptd |
|
56 |
55 5
|
eqeltrrd |
|
57 |
56
|
adantr |
|
58 |
47 53 54 57
|
iblss |
|
59 |
|
ax-resscn |
|
60 |
|
ssid |
|
61 |
|
cncfss |
|
62 |
59 60 61
|
mp2an |
|
63 |
|
abscncf |
|
64 |
62 63
|
sselii |
|
65 |
64
|
a1i |
|
66 |
55
|
reseq1d |
|
67 |
66
|
adantr |
|
68 |
47
|
resmptd |
|
69 |
67 68
|
eqtrd |
|
70 |
4
|
adantr |
|
71 |
|
rescncf |
|
72 |
47 70 71
|
sylc |
|
73 |
69 72
|
eqeltrrd |
|
74 |
65 73
|
cncfmpt1f |
|
75 |
|
cnmbf |
|
76 |
52 74 75
|
sylancr |
|
77 |
51 58
|
itgcl |
|
78 |
77
|
cjcld |
|
79 |
|
ioossre |
|
80 |
79 59
|
sstri |
|
81 |
|
cncfmptc |
|
82 |
80 60 81
|
mp3an23 |
|
83 |
78 82
|
syl |
|
84 |
|
nfcv |
|
85 |
|
nfcsb1v |
|
86 |
|
csbeq1a |
|
87 |
84 85 86
|
cbvmpt |
|
88 |
87 73
|
eqeltrrid |
|
89 |
83 88
|
mulcncf |
|
90 |
|
cnmbf |
|
91 |
52 89 90
|
sylancr |
|
92 |
51 58 76 91
|
itgabsnc |
|
93 |
51
|
abscld |
|
94 |
|
fvexd |
|
95 |
94 58 76
|
iblabsnc |
|
96 |
51
|
absge0d |
|
97 |
93 95 96
|
itgposval |
|
98 |
92 97
|
breqtrd |
|
99 |
|
itgeq1 |
|
100 |
99
|
fveq2d |
|
101 |
|
eleq2 |
|
102 |
101
|
ifbid |
|
103 |
102
|
mpteq2dv |
|
104 |
103
|
fveq2d |
|
105 |
100 104
|
breq12d |
|
106 |
98 105
|
syl5ibcom |
|
107 |
33 106
|
sylbid |
|
108 |
107
|
rexlimdva |
|
109 |
27 108
|
syl5 |
|
110 |
109
|
ralrimiv |
|
111 |
17 1 2 3 18 20 5 22 110
|
ftc1anc |
|
112 |
|
cncff |
|
113 |
6 112
|
syl |
|
114 |
113
|
feqmptd |
|
115 |
114 6
|
eqeltrrd |
|
116 |
14 16 111 115
|
cncfmpt2f |
|
117 |
59
|
a1i |
|
118 |
|
iccssre |
|
119 |
1 2 118
|
syl2anc |
|
120 |
|
fvexd |
|
121 |
2
|
adantr |
|
122 |
121
|
rexrd |
|
123 |
|
elicc2 |
|
124 |
1 2 123
|
syl2anc |
|
125 |
124
|
biimpa |
|
126 |
125
|
simp3d |
|
127 |
|
iooss2 |
|
128 |
122 126 127
|
syl2anc |
|
129 |
|
ioombl |
|
130 |
129
|
a1i |
|
131 |
|
fvexd |
|
132 |
56
|
adantr |
|
133 |
128 130 131 132
|
iblss |
|
134 |
120 133
|
itgcl |
|
135 |
113
|
ffvelrnda |
|
136 |
134 135
|
subcld |
|
137 |
14
|
tgioo2 |
|
138 |
|
iccntr |
|
139 |
1 2 138
|
syl2anc |
|
140 |
117 119 136 137 14 139
|
dvmptntr |
|
141 |
|
reelprrecn |
|
142 |
141
|
a1i |
|
143 |
|
ioossicc |
|
144 |
143
|
sseli |
|
145 |
144 134
|
sylan2 |
|
146 |
22
|
ffvelrnda |
|
147 |
17 1 2 3 4 5
|
ftc1cnnc |
|
148 |
117 119 134 137 14 139
|
dvmptntr |
|
149 |
22
|
feqmptd |
|
150 |
147 148 149
|
3eqtr3d |
|
151 |
144 135
|
sylan2 |
|
152 |
114
|
oveq2d |
|
153 |
117 119 135 137 14 139
|
dvmptntr |
|
154 |
152 149 153
|
3eqtr3rd |
|
155 |
142 145 146 150 151 146 154
|
dvmptsub |
|
156 |
146
|
subidd |
|
157 |
156
|
mpteq2dva |
|
158 |
140 155 157
|
3eqtrd |
|
159 |
|
fconstmpt |
|
160 |
158 159
|
eqtr4di |
|
161 |
1 2 116 160
|
dveq0 |
|
162 |
161
|
fveq1d |
|
163 |
|
oveq2 |
|
164 |
|
itgeq1 |
|
165 |
163 164
|
syl |
|
166 |
|
fveq2 |
|
167 |
165 166
|
oveq12d |
|
168 |
|
eqid |
|
169 |
|
ovex |
|
170 |
167 168 169
|
fvmpt |
|
171 |
10 170
|
syl |
|
172 |
162 171
|
eqtr3d |
|
173 |
|
lbicc2 |
|
174 |
7 8 3 173
|
syl3anc |
|
175 |
|
oveq2 |
|
176 |
|
iooid |
|
177 |
175 176
|
eqtrdi |
|
178 |
|
itgeq1 |
|
179 |
177 178
|
syl |
|
180 |
|
itg0 |
|
181 |
179 180
|
eqtrdi |
|
182 |
|
fveq2 |
|
183 |
181 182
|
oveq12d |
|
184 |
|
df-neg |
|
185 |
183 184
|
eqtr4di |
|
186 |
|
negex |
|
187 |
185 168 186
|
fvmpt |
|
188 |
174 187
|
syl |
|
189 |
13 172 188
|
3eqtr3d |
|
190 |
189
|
oveq2d |
|
191 |
113 10
|
ffvelrnd |
|
192 |
|
fvexd |
|
193 |
192 56
|
itgcl |
|
194 |
191 193
|
pncan3d |
|
195 |
113 174
|
ffvelrnd |
|
196 |
191 195
|
negsubd |
|
197 |
190 194 196
|
3eqtr3d |
|