Step |
Hyp |
Ref |
Expression |
1 |
|
asinf |
|
2 |
1
|
a1i |
|
3 |
|
ioossre |
|
4 |
|
ax-resscn |
|
5 |
3 4
|
sstri |
|
6 |
5
|
a1i |
|
7 |
2 6
|
feqresmpt |
|
8 |
7
|
oveq2d |
|
9 |
|
eqid |
|
10 |
|
reelprrecn |
|
11 |
10
|
a1i |
|
12 |
9
|
recld2 |
|
13 |
|
neg1rr |
|
14 |
|
iocmnfcld |
|
15 |
13 14
|
ax-mp |
|
16 |
|
1re |
|
17 |
|
icopnfcld |
|
18 |
16 17
|
ax-mp |
|
19 |
|
uncld |
|
20 |
15 18 19
|
mp2an |
|
21 |
9
|
tgioo2 |
|
22 |
21
|
fveq2i |
|
23 |
20 22
|
eleqtri |
|
24 |
|
restcldr |
|
25 |
12 23 24
|
mp2an |
|
26 |
9
|
cnfldtopon |
|
27 |
26
|
toponunii |
|
28 |
27
|
cldopn |
|
29 |
25 28
|
mp1i |
|
30 |
|
incom |
|
31 |
|
eqid |
|
32 |
31
|
asindmre |
|
33 |
30 32
|
eqtri |
|
34 |
33
|
a1i |
|
35 |
|
eldifi |
|
36 |
|
asincl |
|
37 |
35 36
|
syl |
|
38 |
37
|
adantl |
|
39 |
|
ovexd |
|
40 |
|
difssd |
|
41 |
2 40
|
feqresmpt |
|
42 |
41
|
oveq2d |
|
43 |
31
|
dvasin |
|
44 |
42 43
|
eqtr3di |
|
45 |
9 11 29 34 38 39 44
|
dvmptres3 |
|
46 |
8 45
|
eqtrd |
|
47 |
46
|
mptru |
|