Step |
Hyp |
Ref |
Expression |
1 |
|
opnbnd.1 |
|
2 |
1
|
iscld3 |
|
3 |
|
eqimss |
|
4 |
2 3
|
syl6bi |
|
5 |
|
ssinss1 |
|
6 |
4 5
|
syl6 |
|
7 |
|
sslin |
|
8 |
7
|
adantl |
|
9 |
|
incom |
|
10 |
|
disjdif |
|
11 |
9 10
|
eqtri |
|
12 |
|
sseq0 |
|
13 |
8 11 12
|
sylancl |
|
14 |
13
|
ex |
|
15 |
|
incom |
|
16 |
|
dfss4 |
|
17 |
|
fveq2 |
|
18 |
17
|
eqcomd |
|
19 |
16 18
|
sylbi |
|
20 |
19
|
adantl |
|
21 |
20
|
ineq2d |
|
22 |
15 21
|
syl5eq |
|
23 |
22
|
ineq2d |
|
24 |
23
|
eqeq1d |
|
25 |
|
difss |
|
26 |
1
|
opnbnd |
|
27 |
25 26
|
mpan2 |
|
28 |
27
|
adantr |
|
29 |
24 28
|
bitr4d |
|
30 |
1
|
opncld |
|
31 |
30
|
ex |
|
32 |
31
|
adantr |
|
33 |
|
eleq1 |
|
34 |
16 33
|
sylbi |
|
35 |
34
|
adantl |
|
36 |
32 35
|
sylibd |
|
37 |
29 36
|
sylbid |
|
38 |
14 37
|
syld |
|
39 |
6 38
|
impbid |
|