Step |
Hyp |
Ref |
Expression |
1 |
|
metdscn.f |
|
2 |
|
metdscn.j |
|
3 |
|
metdscn2.k |
|
4 |
|
eqid |
|
5 |
4
|
xrsdsre |
|
6 |
4
|
xrsxmet |
|
7 |
|
ressxr |
|
8 |
|
eqid |
|
9 |
|
eqid |
|
10 |
|
eqid |
|
11 |
8 9 10
|
metrest |
|
12 |
6 7 11
|
mp2an |
|
13 |
5 12
|
tgioo |
|
14 |
3
|
tgioo2 |
|
15 |
13 14
|
eqtr3i |
|
16 |
15
|
oveq2i |
|
17 |
3
|
cnfldtop |
|
18 |
|
cnrest2r |
|
19 |
17 18
|
ax-mp |
|
20 |
16 19
|
eqsstri |
|
21 |
|
metxmet |
|
22 |
1 2 4 9
|
metdscn |
|
23 |
21 22
|
sylan |
|
24 |
23
|
3adant3 |
|
25 |
1
|
metdsre |
|
26 |
|
frn |
|
27 |
9
|
mopntopon |
|
28 |
6 27
|
ax-mp |
|
29 |
|
cnrest2 |
|
30 |
28 7 29
|
mp3an13 |
|
31 |
25 26 30
|
3syl |
|
32 |
24 31
|
mpbid |
|
33 |
20 32
|
sselid |
|