Step |
Hyp |
Ref |
Expression |
1 |
|
inundif |
|
2 |
1
|
fveq2i |
|
3 |
|
inmbl |
|
4 |
3
|
adantr |
|
5 |
|
difmbl |
|
6 |
5
|
adantr |
|
7 |
|
indifcom |
|
8 |
|
difin0 |
|
9 |
8
|
ineq2i |
|
10 |
|
in0 |
|
11 |
9 10
|
eqtri |
|
12 |
7 11
|
eqtri |
|
13 |
12
|
a1i |
|
14 |
|
mblvol |
|
15 |
4 14
|
syl |
|
16 |
|
inss1 |
|
17 |
16
|
a1i |
|
18 |
|
mblss |
|
19 |
18
|
ad2antrr |
|
20 |
|
mblvol |
|
21 |
20
|
ad2antrr |
|
22 |
|
simprl |
|
23 |
21 22
|
eqeltrrd |
|
24 |
|
ovolsscl |
|
25 |
17 19 23 24
|
syl3anc |
|
26 |
15 25
|
eqeltrd |
|
27 |
|
mblvol |
|
28 |
6 27
|
syl |
|
29 |
|
difssd |
|
30 |
|
ovolsscl |
|
31 |
29 19 23 30
|
syl3anc |
|
32 |
28 31
|
eqeltrd |
|
33 |
|
volun |
|
34 |
4 6 13 26 32 33
|
syl32anc |
|
35 |
2 34
|
syl5eqr |
|
36 |
35
|
oveq1d |
|
37 |
26
|
recnd |
|
38 |
32
|
recnd |
|
39 |
|
simprr |
|
40 |
39
|
recnd |
|
41 |
37 38 40
|
addassd |
|
42 |
|
undif1 |
|
43 |
42
|
fveq2i |
|
44 |
|
simplr |
|
45 |
|
incom |
|
46 |
|
disjdif |
|
47 |
45 46
|
eqtri |
|
48 |
47
|
a1i |
|
49 |
|
volun |
|
50 |
6 44 48 32 39 49
|
syl32anc |
|
51 |
43 50
|
syl5reqr |
|
52 |
51
|
oveq2d |
|
53 |
36 41 52
|
3eqtrd |
|