Step |
Hyp |
Ref |
Expression |
1 |
|
cmslssbn.x |
|
2 |
|
cmscsscms.s |
|
3 |
|
cmsms |
|
4 |
3
|
adantr |
|
5 |
|
ressms |
|
6 |
4 5
|
sylan |
|
7 |
1 6
|
eqeltrid |
|
8 |
|
cphlmod |
|
9 |
8
|
adantl |
|
10 |
9
|
adantr |
|
11 |
|
cphphl |
|
12 |
11
|
adantl |
|
13 |
|
eqid |
|
14 |
2 13
|
csslss |
|
15 |
12 14
|
sylan |
|
16 |
13
|
lsssubg |
|
17 |
10 15 16
|
syl2anc |
|
18 |
1
|
subgbas |
|
19 |
17 18
|
syl |
|
20 |
|
eqid |
|
21 |
2 20
|
csscld |
|
22 |
21
|
adantll |
|
23 |
19 22
|
eqeltrrd |
|
24 |
|
eqid |
|
25 |
1 24
|
ressds |
|
26 |
25
|
adantl |
|
27 |
26
|
eqcomd |
|
28 |
27
|
reseq1d |
|
29 |
19 17
|
eqeltrrd |
|
30 |
|
eqid |
|
31 |
30
|
subgss |
|
32 |
29 31
|
syl |
|
33 |
|
xpss12 |
|
34 |
32 32 33
|
syl2anc |
|
35 |
34
|
resabs1d |
|
36 |
28 35
|
eqtr4d |
|
37 |
36
|
eleq1d |
|
38 |
|
eqid |
|
39 |
30 38
|
cmscmet |
|
40 |
39
|
adantr |
|
41 |
40
|
adantr |
|
42 |
|
eqid |
|
43 |
42
|
cmetss |
|
44 |
41 43
|
syl |
|
45 |
4
|
adantr |
|
46 |
20 30 38
|
mstopn |
|
47 |
45 46
|
syl |
|
48 |
47
|
eqcomd |
|
49 |
48
|
fveq2d |
|
50 |
49
|
eleq2d |
|
51 |
37 44 50
|
3bitrd |
|
52 |
23 51
|
mpbird |
|
53 |
|
eqid |
|
54 |
|
eqid |
|
55 |
53 54
|
iscms |
|
56 |
7 52 55
|
sylanbrc |
|