Step |
Hyp |
Ref |
Expression |
1 |
|
opnbnd.1 |
|
2 |
|
disjdif |
|
3 |
2
|
a1i |
|
4 |
|
ineq1 |
|
5 |
4
|
eqeq1d |
|
6 |
3 5
|
syl5ibcom |
|
7 |
1
|
ntrss2 |
|
8 |
7
|
adantr |
|
9 |
|
inssdif0 |
|
10 |
1
|
sscls |
|
11 |
|
df-ss |
|
12 |
10 11
|
sylib |
|
13 |
12
|
eqcomd |
|
14 |
|
eqimss |
|
15 |
13 14
|
syl |
|
16 |
|
sstr |
|
17 |
15 16
|
sylan |
|
18 |
9 17
|
sylan2br |
|
19 |
8 18
|
eqssd |
|
20 |
19
|
ex |
|
21 |
6 20
|
impbid |
|
22 |
1
|
isopn3 |
|
23 |
1
|
topbnd |
|
24 |
23
|
ineq2d |
|
25 |
24
|
eqeq1d |
|
26 |
21 22 25
|
3bitr4d |
|