Step |
Hyp |
Ref |
Expression |
1 |
|
cmetcusp1.x |
|
2 |
|
cmetcusp1.d |
|
3 |
|
cmetcusp1.u |
|
4 |
|
cmsms |
|
5 |
|
msxms |
|
6 |
4 5
|
syl |
|
7 |
1 2 3
|
xmsusp |
|
8 |
6 7
|
syl3an2 |
|
9 |
|
simpl3 |
|
10 |
9
|
fveq2d |
|
11 |
10
|
eleq2d |
|
12 |
|
simpl1 |
|
13 |
1 2
|
cmscmet |
|
14 |
|
cmetmet |
|
15 |
|
metxmet |
|
16 |
13 14 15
|
3syl |
|
17 |
16
|
3ad2ant2 |
|
18 |
17
|
adantr |
|
19 |
|
simpr |
|
20 |
|
cfilucfil4 |
|
21 |
12 18 19 20
|
syl3anc |
|
22 |
11 21
|
bitrd |
|
23 |
|
eqid |
|
24 |
23
|
iscmet |
|
25 |
24
|
simprbi |
|
26 |
13 25
|
syl |
|
27 |
|
eqid |
|
28 |
27 1 2
|
xmstopn |
|
29 |
6 28
|
syl |
|
30 |
29
|
oveq1d |
|
31 |
30
|
neeq1d |
|
32 |
31
|
ralbidv |
|
33 |
26 32
|
mpbird |
|
34 |
33
|
r19.21bi |
|
35 |
34
|
ex |
|
36 |
35
|
3ad2ant2 |
|
37 |
36
|
adantr |
|
38 |
22 37
|
sylbid |
|
39 |
38
|
ralrimiva |
|
40 |
1 3 27
|
iscusp2 |
|
41 |
8 39 40
|
sylanbrc |
|