Step |
Hyp |
Ref |
Expression |
1 |
|
hmeores.1 |
|
2 |
|
hmeocn |
|
3 |
2
|
adantr |
|
4 |
1
|
cnrest |
|
5 |
3 4
|
sylancom |
|
6 |
|
cntop2 |
|
7 |
3 6
|
syl |
|
8 |
|
eqid |
|
9 |
8
|
toptopon |
|
10 |
7 9
|
sylib |
|
11 |
|
df-ima |
|
12 |
11
|
eqimss2i |
|
13 |
12
|
a1i |
|
14 |
|
imassrn |
|
15 |
1 8
|
cnf |
|
16 |
3 15
|
syl |
|
17 |
16
|
frnd |
|
18 |
14 17
|
sstrid |
|
19 |
|
cnrest2 |
|
20 |
10 13 18 19
|
syl3anc |
|
21 |
5 20
|
mpbid |
|
22 |
|
hmeocnvcn |
|
23 |
22
|
adantr |
|
24 |
8 1
|
cnf |
|
25 |
|
ffun |
|
26 |
|
funcnvres |
|
27 |
23 24 25 26
|
4syl |
|
28 |
8
|
cnrest |
|
29 |
23 18 28
|
syl2anc |
|
30 |
27 29
|
eqeltrd |
|
31 |
|
cntop1 |
|
32 |
3 31
|
syl |
|
33 |
1
|
toptopon |
|
34 |
32 33
|
sylib |
|
35 |
|
dfdm4 |
|
36 |
|
fssres |
|
37 |
16 36
|
sylancom |
|
38 |
37
|
fdmd |
|
39 |
35 38
|
syl5eqr |
|
40 |
|
eqimss |
|
41 |
39 40
|
syl |
|
42 |
|
simpr |
|
43 |
|
cnrest2 |
|
44 |
34 41 42 43
|
syl3anc |
|
45 |
30 44
|
mpbid |
|
46 |
|
ishmeo |
|
47 |
21 45 46
|
sylanbrc |
|