Step |
Hyp |
Ref |
Expression |
1 |
|
iunin1 |
|
2 |
|
uniiun |
|
3 |
2
|
ineq1i |
|
4 |
1 3
|
eqtr4i |
|
5 |
4
|
fveq2i |
|
6 |
|
simplll |
|
7 |
|
nfv |
|
8 |
|
nfv |
|
9 |
|
nfdisj1 |
|
10 |
8 9
|
nfan |
|
11 |
7 10
|
nfan |
|
12 |
|
simp1ll |
|
13 |
|
measbase |
|
14 |
12 13
|
syl |
|
15 |
|
simp3 |
|
16 |
|
simp1r |
|
17 |
|
elelpwi |
|
18 |
15 16 17
|
syl2anc |
|
19 |
|
simp1lr |
|
20 |
|
inelsiga |
|
21 |
14 18 19 20
|
syl3anc |
|
22 |
21
|
3expia |
|
23 |
11 22
|
ralrimi |
|
24 |
|
simprl |
|
25 |
|
disjin |
|
26 |
25
|
ad2antll |
|
27 |
|
measvuni |
|
28 |
6 23 24 26 27
|
syl112anc |
|
29 |
5 28
|
eqtr3id |
|