Step |
Hyp |
Ref |
Expression |
1 |
|
voliunlem.3 |
|
2 |
|
voliunlem.5 |
|
3 |
|
voliunlem1.6 |
|
4 |
|
voliunlem1.7 |
|
5 |
|
voliunlem1.8 |
|
6 |
|
difss |
|
7 |
5
|
adantr |
|
8 |
|
ovolsscl |
|
9 |
6 4 7 8
|
mp3an2ani |
|
10 |
|
difss |
|
11 |
|
ovolsscl |
|
12 |
10 4 7 11
|
mp3an2ani |
|
13 |
|
inss1 |
|
14 |
|
ovolsscl |
|
15 |
13 4 7 14
|
mp3an2ani |
|
16 |
|
elfznn |
|
17 |
1
|
ffnd |
|
18 |
|
fnfvelrn |
|
19 |
17 18
|
sylan |
|
20 |
|
elssuni |
|
21 |
19 20
|
syl |
|
22 |
16 21
|
sylan2 |
|
23 |
22
|
ralrimiva |
|
24 |
23
|
adantr |
|
25 |
|
iunss |
|
26 |
24 25
|
sylibr |
|
27 |
26
|
sscond |
|
28 |
4
|
adantr |
|
29 |
10 28
|
sstrid |
|
30 |
|
ovolss |
|
31 |
27 29 30
|
syl2anc |
|
32 |
9 12 15 31
|
leadd2dd |
|
33 |
|
oveq2 |
|
34 |
33
|
iuneq1d |
|
35 |
34
|
eleq1d |
|
36 |
34
|
ineq2d |
|
37 |
36
|
fveq2d |
|
38 |
|
fveq2 |
|
39 |
37 38
|
eqeq12d |
|
40 |
35 39
|
anbi12d |
|
41 |
40
|
imbi2d |
|
42 |
|
oveq2 |
|
43 |
42
|
iuneq1d |
|
44 |
43
|
eleq1d |
|
45 |
43
|
ineq2d |
|
46 |
45
|
fveq2d |
|
47 |
|
fveq2 |
|
48 |
46 47
|
eqeq12d |
|
49 |
44 48
|
anbi12d |
|
50 |
49
|
imbi2d |
|
51 |
|
oveq2 |
|
52 |
51
|
iuneq1d |
|
53 |
52
|
eleq1d |
|
54 |
52
|
ineq2d |
|
55 |
54
|
fveq2d |
|
56 |
|
fveq2 |
|
57 |
55 56
|
eqeq12d |
|
58 |
53 57
|
anbi12d |
|
59 |
58
|
imbi2d |
|
60 |
|
1z |
|
61 |
|
fzsn |
|
62 |
|
iuneq1 |
|
63 |
60 61 62
|
mp2b |
|
64 |
|
1ex |
|
65 |
|
fveq2 |
|
66 |
64 65
|
iunxsn |
|
67 |
63 66
|
eqtri |
|
68 |
|
1nn |
|
69 |
|
ffvelrn |
|
70 |
1 68 69
|
sylancl |
|
71 |
67 70
|
eqeltrid |
|
72 |
65
|
ineq2d |
|
73 |
72
|
fveq2d |
|
74 |
|
fvex |
|
75 |
73 3 74
|
fvmpt |
|
76 |
68 75
|
ax-mp |
|
77 |
|
seq1 |
|
78 |
60 77
|
ax-mp |
|
79 |
67
|
ineq2i |
|
80 |
79
|
fveq2i |
|
81 |
76 78 80
|
3eqtr4ri |
|
82 |
71 81
|
jctir |
|
83 |
|
peano2nn |
|
84 |
|
ffvelrn |
|
85 |
1 83 84
|
syl2an |
|
86 |
|
unmbl |
|
87 |
86
|
ex |
|
88 |
85 87
|
syl5com |
|
89 |
|
simpr |
|
90 |
|
nnuz |
|
91 |
89 90
|
eleqtrdi |
|
92 |
|
fzsuc |
|
93 |
|
iuneq1 |
|
94 |
91 92 93
|
3syl |
|
95 |
|
iunxun |
|
96 |
|
ovex |
|
97 |
|
fveq2 |
|
98 |
96 97
|
iunxsn |
|
99 |
98
|
uneq2i |
|
100 |
95 99
|
eqtri |
|
101 |
94 100
|
eqtrdi |
|
102 |
101
|
eleq1d |
|
103 |
88 102
|
sylibrd |
|
104 |
|
oveq1 |
|
105 |
|
inss1 |
|
106 |
105 28
|
sstrid |
|
107 |
|
ovolsscl |
|
108 |
105 4 7 107
|
mp3an2ani |
|
109 |
|
mblsplit |
|
110 |
85 106 108 109
|
syl3anc |
|
111 |
|
in32 |
|
112 |
|
inss2 |
|
113 |
83
|
adantl |
|
114 |
113 90
|
eleqtrdi |
|
115 |
|
eluzfz2 |
|
116 |
97
|
ssiun2s |
|
117 |
114 115 116
|
3syl |
|
118 |
112 117
|
sstrid |
|
119 |
|
df-ss |
|
120 |
118 119
|
sylib |
|
121 |
111 120
|
syl5eq |
|
122 |
121
|
fveq2d |
|
123 |
|
indif2 |
|
124 |
|
uncom |
|
125 |
101 124
|
eqtr2di |
|
126 |
2
|
ad2antrr |
|
127 |
113
|
adantr |
|
128 |
16
|
adantl |
|
129 |
128
|
nnred |
|
130 |
|
elfzle2 |
|
131 |
130
|
adantl |
|
132 |
89
|
adantr |
|
133 |
|
nnleltp1 |
|
134 |
128 132 133
|
syl2anc |
|
135 |
131 134
|
mpbid |
|
136 |
129 135
|
gtned |
|
137 |
|
fveq2 |
|
138 |
|
fveq2 |
|
139 |
137 138
|
disji2 |
|
140 |
126 127 128 136 139
|
syl121anc |
|
141 |
140
|
iuneq2dv |
|
142 |
|
iunin2 |
|
143 |
|
iun0 |
|
144 |
141 142 143
|
3eqtr3g |
|
145 |
|
uneqdifeq |
|
146 |
117 144 145
|
syl2anc |
|
147 |
125 146
|
mpbid |
|
148 |
147
|
ineq2d |
|
149 |
123 148
|
syl5eqr |
|
150 |
149
|
fveq2d |
|
151 |
122 150
|
oveq12d |
|
152 |
|
inss1 |
|
153 |
|
ovolsscl |
|
154 |
152 4 7 153
|
mp3an2ani |
|
155 |
154
|
recnd |
|
156 |
15
|
recnd |
|
157 |
155 156
|
addcomd |
|
158 |
110 151 157
|
3eqtrd |
|
159 |
|
seqp1 |
|
160 |
91 159
|
syl |
|
161 |
97
|
ineq2d |
|
162 |
161
|
fveq2d |
|
163 |
|
fvex |
|
164 |
162 3 163
|
fvmpt |
|
165 |
113 164
|
syl |
|
166 |
165
|
oveq2d |
|
167 |
160 166
|
eqtrd |
|
168 |
158 167
|
eqeq12d |
|
169 |
104 168
|
syl5ibr |
|
170 |
103 169
|
anim12d |
|
171 |
170
|
expcom |
|
172 |
171
|
a2d |
|
173 |
41 50 59 50 82 172
|
nnind |
|
174 |
173
|
impcom |
|
175 |
174
|
simprd |
|
176 |
175
|
eqcomd |
|
177 |
176
|
oveq1d |
|
178 |
174
|
simpld |
|
179 |
|
mblsplit |
|
180 |
178 28 7 179
|
syl3anc |
|
181 |
32 177 180
|
3brtr4d |
|