Step |
Hyp |
Ref |
Expression |
1 |
|
dfral2 |
|
2 |
|
iunfi |
|
3 |
|
iunin2 |
|
4 |
3
|
eleq1i |
|
5 |
|
uniiun |
|
6 |
5
|
eqcomi |
|
7 |
6
|
ineq2i |
|
8 |
7
|
eleq1i |
|
9 |
|
df-ss |
|
10 |
|
eleq1 |
|
11 |
|
pm2.24 |
|
12 |
10 11
|
syl6bi |
|
13 |
9 12
|
sylbi |
|
14 |
13
|
com12 |
|
15 |
8 14
|
sylbi |
|
16 |
4 15
|
sylbi |
|
17 |
2 16
|
syl |
|
18 |
17
|
ex |
|
19 |
18
|
com24 |
|
20 |
19
|
3imp21 |
|
21 |
1 20
|
syl5bir |
|
22 |
21
|
pm2.18d |
|