Step |
Hyp |
Ref |
Expression |
1 |
|
metdscn.f |
|
2 |
|
metdscn.j |
|
3 |
|
metdscn.c |
|
4 |
|
metdscn.k |
|
5 |
1
|
metdsf |
|
6 |
|
iccssxr |
|
7 |
|
fss |
|
8 |
5 6 7
|
sylancl |
|
9 |
|
simprr |
|
10 |
8
|
ad2antrr |
|
11 |
|
simplrl |
|
12 |
10 11
|
ffvelrnd |
|
13 |
|
simprl |
|
14 |
10 13
|
ffvelrnd |
|
15 |
3
|
xrsdsval |
|
16 |
12 14 15
|
syl2anc |
|
17 |
|
simplll |
|
18 |
|
simpllr |
|
19 |
|
simplrr |
|
20 |
|
xmetsym |
|
21 |
17 13 11 20
|
syl3anc |
|
22 |
|
simprr |
|
23 |
21 22
|
eqbrtrd |
|
24 |
1 2 3 4 17 18 13 11 19 23
|
metdscnlem |
|
25 |
1 2 3 4 17 18 11 13 19 22
|
metdscnlem |
|
26 |
|
breq1 |
|
27 |
|
breq1 |
|
28 |
26 27
|
ifboth |
|
29 |
24 25 28
|
syl2anc |
|
30 |
16 29
|
eqbrtrd |
|
31 |
30
|
expr |
|
32 |
31
|
ralrimiva |
|
33 |
|
breq2 |
|
34 |
33
|
rspceaimv |
|
35 |
9 32 34
|
syl2anc |
|
36 |
35
|
ralrimivva |
|
37 |
|
simpl |
|
38 |
3
|
xrsxmet |
|
39 |
2 4
|
metcn |
|
40 |
37 38 39
|
sylancl |
|
41 |
8 36 40
|
mpbir2and |
|