Step |
Hyp |
Ref |
Expression |
1 |
|
cmetmet |
|
2 |
|
metxmet |
|
3 |
|
xmetpsmet |
|
4 |
1 2 3
|
3syl |
|
5 |
4
|
anim2i |
|
6 |
|
metuust |
|
7 |
|
eqid |
|
8 |
7
|
tususp |
|
9 |
5 6 8
|
3syl |
|
10 |
|
simpll |
|
11 |
10
|
simprd |
|
12 |
1 2
|
syl |
|
13 |
12
|
ad3antlr |
|
14 |
7
|
tusbas |
|
15 |
14
|
fveq2d |
|
16 |
15
|
eleq2d |
|
17 |
5 6 16
|
3syl |
|
18 |
17
|
biimpar |
|
19 |
18
|
adantr |
|
20 |
7
|
tususs |
|
21 |
20
|
fveq2d |
|
22 |
5 6 21
|
3syl |
|
23 |
22
|
eleq2d |
|
24 |
23
|
biimpar |
|
25 |
24
|
adantlr |
|
26 |
|
cfilucfil2 |
|
27 |
5 26
|
syl |
|
28 |
27
|
simplbda |
|
29 |
10 25 28
|
syl2anc |
|
30 |
|
iscfil |
|
31 |
30
|
biimpar |
|
32 |
13 19 29 31
|
syl12anc |
|
33 |
|
eqid |
|
34 |
33
|
cmetcvg |
|
35 |
11 32 34
|
syl2anc |
|
36 |
|
eqid |
|
37 |
7 36
|
tustopn |
|
38 |
5 6 37
|
3syl |
|
39 |
12
|
anim2i |
|
40 |
|
xmetutop |
|
41 |
39 40
|
syl |
|
42 |
38 41
|
eqtr3d |
|
43 |
42
|
oveq1d |
|
44 |
43
|
neeq1d |
|
45 |
44
|
biimpar |
|
46 |
10 35 45
|
syl2anc |
|
47 |
46
|
ex |
|
48 |
47
|
ralrimiva |
|
49 |
|
iscusp |
|
50 |
9 48 49
|
sylanbrc |
|