Step |
Hyp |
Ref |
Expression |
1 |
|
tmdcn2.1 |
|
2 |
|
tmdcn2.2 |
|
3 |
|
tmdcn2.3 |
|
4 |
2 1
|
tmdtopon |
|
5 |
4
|
ad2antrr |
|
6 |
|
eqid |
|
7 |
2 6
|
tmdcn |
|
8 |
7
|
ad2antrr |
|
9 |
|
simpr1 |
|
10 |
|
simpr2 |
|
11 |
9 10
|
opelxpd |
|
12 |
|
txtopon |
|
13 |
5 5 12
|
syl2anc |
|
14 |
|
toponuni |
|
15 |
13 14
|
syl |
|
16 |
11 15
|
eleqtrd |
|
17 |
|
eqid |
|
18 |
17
|
cncnpi |
|
19 |
8 16 18
|
syl2anc |
|
20 |
|
simplr |
|
21 |
1 3 6
|
plusfval |
|
22 |
9 10 21
|
syl2anc |
|
23 |
|
simpr3 |
|
24 |
22 23
|
eqeltrd |
|
25 |
5 5 19 20 9 10 24
|
txcnpi |
|
26 |
|
dfss3 |
|
27 |
|
eleq1 |
|
28 |
1 6
|
plusffn |
|
29 |
|
elpreima |
|
30 |
28 29
|
ax-mp |
|
31 |
27 30
|
bitrdi |
|
32 |
31
|
ralxp |
|
33 |
26 32
|
bitri |
|
34 |
|
opelxp |
|
35 |
|
df-ov |
|
36 |
1 3 6
|
plusfval |
|
37 |
35 36
|
syl5eqr |
|
38 |
34 37
|
sylbi |
|
39 |
38
|
eleq1d |
|
40 |
39
|
biimpa |
|
41 |
40
|
2ralimi |
|
42 |
33 41
|
sylbi |
|
43 |
42
|
3anim3i |
|
44 |
43
|
reximi |
|
45 |
44
|
reximi |
|
46 |
25 45
|
syl |
|