Step |
Hyp |
Ref |
Expression |
1 |
|
bndth.1 |
|
2 |
|
bndth.2 |
|
3 |
|
bndth.3 |
|
4 |
|
bndth.4 |
|
5 |
|
evth.5 |
|
6 |
|
cmptop |
|
7 |
3 6
|
syl |
|
8 |
1
|
toptopon |
|
9 |
7 8
|
sylib |
|
10 |
|
uniretop |
|
11 |
2
|
unieqi |
|
12 |
10 11
|
eqtr4i |
|
13 |
1 12
|
cnf |
|
14 |
4 13
|
syl |
|
15 |
14
|
feqmptd |
|
16 |
15 4
|
eqeltrrd |
|
17 |
|
retopon |
|
18 |
2 17
|
eqeltri |
|
19 |
18
|
a1i |
|
20 |
|
eqid |
|
21 |
20
|
cnfldtopon |
|
22 |
21
|
a1i |
|
23 |
|
0cnd |
|
24 |
19 22 23
|
cnmptc |
|
25 |
20
|
tgioo2 |
|
26 |
2 25
|
eqtri |
|
27 |
|
ax-resscn |
|
28 |
27
|
a1i |
|
29 |
22
|
cnmptid |
|
30 |
26 22 28 29
|
cnmpt1res |
|
31 |
20
|
subcn |
|
32 |
31
|
a1i |
|
33 |
19 24 30 32
|
cnmpt12f |
|
34 |
|
df-neg |
|
35 |
|
renegcl |
|
36 |
34 35
|
eqeltrrid |
|
37 |
36
|
adantl |
|
38 |
37
|
fmpttd |
|
39 |
38
|
frnd |
|
40 |
|
cnrest2 |
|
41 |
22 39 28 40
|
syl3anc |
|
42 |
33 41
|
mpbid |
|
43 |
26
|
oveq2i |
|
44 |
42 43
|
eleqtrrdi |
|
45 |
|
negeq |
|
46 |
34 45
|
syl5eqr |
|
47 |
9 16 19 44 46
|
cnmpt11 |
|
48 |
1 2 3 47 5
|
evth |
|
49 |
|
fveq2 |
|
50 |
49
|
negeqd |
|
51 |
|
eqid |
|
52 |
|
negex |
|
53 |
50 51 52
|
fvmpt |
|
54 |
53
|
adantl |
|
55 |
|
fveq2 |
|
56 |
55
|
negeqd |
|
57 |
|
negex |
|
58 |
56 51 57
|
fvmpt |
|
59 |
58
|
ad2antlr |
|
60 |
54 59
|
breq12d |
|
61 |
14
|
ffvelrnda |
|
62 |
61
|
adantr |
|
63 |
14
|
ffvelrnda |
|
64 |
63
|
adantlr |
|
65 |
62 64
|
lenegd |
|
66 |
60 65
|
bitr4d |
|
67 |
66
|
ralbidva |
|
68 |
67
|
rexbidva |
|
69 |
48 68
|
mpbid |
|