Step |
Hyp |
Ref |
Expression |
1 |
|
ovolval3.a |
|
2 |
|
ovolval3.m |
|
3 |
|
eqid |
|
4 |
1 3
|
ovolval2 |
|
5 |
|
reex |
|
6 |
5 5
|
xpex |
|
7 |
|
inss2 |
|
8 |
|
mapss |
|
9 |
6 7 8
|
mp2an |
|
10 |
9
|
sseli |
|
11 |
|
elmapi |
|
12 |
10 11
|
syl |
|
13 |
12
|
ffvelrnda |
|
14 |
|
1st2nd2 |
|
15 |
13 14
|
syl |
|
16 |
15
|
fveq2d |
|
17 |
|
df-ov |
|
18 |
17
|
eqcomi |
|
19 |
18
|
a1i |
|
20 |
16 19
|
eqtrd |
|
21 |
20
|
fveq2d |
|
22 |
|
xp1st |
|
23 |
13 22
|
syl |
|
24 |
|
xp2nd |
|
25 |
13 24
|
syl |
|
26 |
|
elmapi |
|
27 |
26
|
adantr |
|
28 |
|
simpr |
|
29 |
|
ovolfcl |
|
30 |
27 28 29
|
syl2anc |
|
31 |
30
|
simp3d |
|
32 |
|
volioo |
|
33 |
23 25 31 32
|
syl3anc |
|
34 |
21 33
|
eqtrd |
|
35 |
|
ioof |
|
36 |
|
ffun |
|
37 |
35 36
|
ax-mp |
|
38 |
37
|
a1i |
|
39 |
|
rexpssxrxp |
|
40 |
39 13
|
sseldi |
|
41 |
35
|
fdmi |
|
42 |
41
|
eqcomi |
|
43 |
42
|
a1i |
|
44 |
40 43
|
eleqtrd |
|
45 |
|
fvco |
|
46 |
38 44 45
|
syl2anc |
|
47 |
15
|
fveq2d |
|
48 |
|
df-ov |
|
49 |
48
|
eqcomi |
|
50 |
49
|
a1i |
|
51 |
23
|
recnd |
|
52 |
25
|
recnd |
|
53 |
|
eqid |
|
54 |
53
|
cnmetdval |
|
55 |
51 52 54
|
syl2anc |
|
56 |
|
abssub |
|
57 |
51 52 56
|
syl2anc |
|
58 |
23 25 31
|
abssubge0d |
|
59 |
55 57 58
|
3eqtrd |
|
60 |
47 50 59
|
3eqtrd |
|
61 |
34 46 60
|
3eqtr4d |
|
62 |
61
|
mpteq2dva |
|
63 |
|
volioof |
|
64 |
63
|
a1i |
|
65 |
39
|
a1i |
|
66 |
12 65
|
fssd |
|
67 |
|
fcompt |
|
68 |
64 66 67
|
syl2anc |
|
69 |
|
absf |
|
70 |
|
subf |
|
71 |
|
fco |
|
72 |
69 70 71
|
mp2an |
|
73 |
72
|
a1i |
|
74 |
|
rr2sscn2 |
|
75 |
74
|
a1i |
|
76 |
12 75
|
fssd |
|
77 |
|
fcompt |
|
78 |
73 76 77
|
syl2anc |
|
79 |
62 68 78
|
3eqtr4d |
|
80 |
79
|
fveq2d |
|
81 |
80
|
eqeq2d |
|
82 |
81
|
anbi2d |
|
83 |
82
|
rexbiia |
|
84 |
83
|
rabbii |
|
85 |
2 84
|
eqtr2i |
|
86 |
85
|
infeq1i |
|
87 |
86
|
a1i |
|
88 |
4 87
|
eqtrd |
|