Step |
Hyp |
Ref |
Expression |
1 |
|
eqid |
|
2 |
1
|
cldss |
|
3 |
|
eqid |
|
4 |
3
|
cldss |
|
5 |
|
xpss12 |
|
6 |
2 4 5
|
syl2an |
|
7 |
|
cldrcl |
|
8 |
|
cldrcl |
|
9 |
1 3
|
txuni |
|
10 |
7 8 9
|
syl2an |
|
11 |
6 10
|
sseqtrd |
|
12 |
|
difxp |
|
13 |
10
|
difeq1d |
|
14 |
12 13
|
syl5eqr |
|
15 |
|
txtop |
|
16 |
7 8 15
|
syl2an |
|
17 |
7
|
adantr |
|
18 |
8
|
adantl |
|
19 |
1
|
cldopn |
|
20 |
19
|
adantr |
|
21 |
3
|
topopn |
|
22 |
18 21
|
syl |
|
23 |
|
txopn |
|
24 |
17 18 20 22 23
|
syl22anc |
|
25 |
1
|
topopn |
|
26 |
17 25
|
syl |
|
27 |
3
|
cldopn |
|
28 |
27
|
adantl |
|
29 |
|
txopn |
|
30 |
17 18 26 28 29
|
syl22anc |
|
31 |
|
unopn |
|
32 |
16 24 30 31
|
syl3anc |
|
33 |
14 32
|
eqeltrrd |
|
34 |
|
eqid |
|
35 |
34
|
iscld |
|
36 |
16 35
|
syl |
|
37 |
11 33 36
|
mpbir2and |
|