Step |
Hyp |
Ref |
Expression |
1 |
|
simp1 |
|
2 |
|
simp2r |
|
3 |
|
measbase |
|
4 |
1 3
|
syl |
|
5 |
|
simp2l |
|
6 |
|
difelsiga |
|
7 |
4 5 2 6
|
syl3anc |
|
8 |
|
prelpwi |
|
9 |
2 7 8
|
syl2anc |
|
10 |
|
prct |
|
11 |
2 7 10
|
syl2anc |
|
12 |
|
simp3 |
|
13 |
|
disjdifprg2 |
|
14 |
|
prcom |
|
15 |
|
dfss |
|
16 |
15
|
biimpi |
|
17 |
|
incom |
|
18 |
16 17
|
eqtrdi |
|
19 |
18
|
preq2d |
|
20 |
14 19
|
syl5eqr |
|
21 |
20
|
disjeq1d |
|
22 |
21
|
biimprd |
|
23 |
13 22
|
mpan9 |
|
24 |
5 12 23
|
syl2anc |
|
25 |
11 24
|
jca |
|
26 |
|
measvun |
|
27 |
1 9 25 26
|
syl3anc |
|
28 |
2 7
|
jca |
|
29 |
|
uniprg |
|
30 |
|
undif |
|
31 |
30
|
biimpi |
|
32 |
29 31
|
sylan9eq |
|
33 |
32
|
fveq2d |
|
34 |
28 12 33
|
syl2anc |
|
35 |
|
simpr |
|
36 |
35
|
fveq2d |
|
37 |
|
simpr |
|
38 |
37
|
fveq2d |
|
39 |
|
measvxrge0 |
|
40 |
1 2 39
|
syl2anc |
|
41 |
|
measvxrge0 |
|
42 |
1 7 41
|
syl2anc |
|
43 |
|
eqimss |
|
44 |
|
ssdifeq0 |
|
45 |
43 44
|
sylib |
|
46 |
45
|
fveq2d |
|
47 |
|
measvnul |
|
48 |
46 47
|
sylan9eqr |
|
49 |
1 48
|
sylan |
|
50 |
49
|
orcd |
|
51 |
50
|
ex |
|
52 |
36 38 2 7 40 42 51
|
esumpr2 |
|
53 |
27 34 52
|
3eqtr3d |
|