Step |
Hyp |
Ref |
Expression |
1 |
|
kmlem9.1 |
|
2 |
1
|
unieqi |
|
3 |
|
vex |
|
4 |
3
|
difexi |
|
5 |
4
|
dfiun2 |
|
6 |
2 5
|
eqtr4i |
|
7 |
6
|
ineq2i |
|
8 |
|
iunin2 |
|
9 |
7 8
|
eqtr4i |
|
10 |
|
undif2 |
|
11 |
|
snssi |
|
12 |
|
ssequn1 |
|
13 |
11 12
|
sylib |
|
14 |
10 13
|
syl5req |
|
15 |
14
|
iuneq1d |
|
16 |
|
iunxun |
|
17 |
|
vex |
|
18 |
|
difeq1 |
|
19 |
|
sneq |
|
20 |
19
|
difeq2d |
|
21 |
20
|
unieqd |
|
22 |
21
|
difeq2d |
|
23 |
18 22
|
eqtrd |
|
24 |
23
|
ineq2d |
|
25 |
17 24
|
iunxsn |
|
26 |
25
|
uneq1i |
|
27 |
16 26
|
eqtri |
|
28 |
|
eldifsni |
|
29 |
|
incom |
|
30 |
|
kmlem4 |
|
31 |
29 30
|
syl5eq |
|
32 |
31
|
ex |
|
33 |
28 32
|
syl5 |
|
34 |
33
|
ralrimiv |
|
35 |
|
iuneq2 |
|
36 |
34 35
|
syl |
|
37 |
|
iun0 |
|
38 |
36 37
|
eqtrdi |
|
39 |
38
|
uneq2d |
|
40 |
27 39
|
syl5eq |
|
41 |
15 40
|
eqtrd |
|
42 |
|
un0 |
|
43 |
|
indif |
|
44 |
42 43
|
eqtri |
|
45 |
41 44
|
eqtrdi |
|
46 |
9 45
|
syl5eq |
|