Step |
Hyp |
Ref |
Expression |
1 |
|
metust.1 |
|
2 |
|
relres |
|
3 |
2
|
a1i |
|
4 |
|
vex |
|
5 |
4
|
brresi |
|
6 |
|
df-br |
|
7 |
4
|
ideq |
|
8 |
7
|
anbi2i |
|
9 |
5 6 8
|
3bitr3i |
|
10 |
9
|
biimpi |
|
11 |
10
|
ad2antlr |
|
12 |
11
|
simprd |
|
13 |
|
df-ov |
|
14 |
|
opeq2 |
|
15 |
14
|
fveq2d |
|
16 |
13 15
|
syl5eq |
|
17 |
12 16
|
syl |
|
18 |
|
simplll |
|
19 |
11
|
simpld |
|
20 |
|
psmet0 |
|
21 |
18 19 20
|
syl2anc |
|
22 |
17 21
|
eqtr3d |
|
23 |
|
0xr |
|
24 |
|
rpxr |
|
25 |
|
rpgt0 |
|
26 |
|
lbico1 |
|
27 |
23 24 25 26
|
mp3an2i |
|
28 |
27
|
adantl |
|
29 |
22 28
|
eqeltrd |
|
30 |
|
psmetf |
|
31 |
30
|
ffund |
|
32 |
31
|
ad3antrrr |
|
33 |
12 19
|
eqeltrrd |
|
34 |
19 33
|
opelxpd |
|
35 |
30
|
fdmd |
|
36 |
35
|
ad3antrrr |
|
37 |
34 36
|
eleqtrrd |
|
38 |
|
fvimacnv |
|
39 |
32 37 38
|
syl2anc |
|
40 |
29 39
|
mpbid |
|
41 |
40
|
adantr |
|
42 |
|
simpr |
|
43 |
41 42
|
eleqtrrd |
|
44 |
|
simplr |
|
45 |
1
|
metustel |
|
46 |
45
|
ad2antrr |
|
47 |
44 46
|
mpbid |
|
48 |
43 47
|
r19.29a |
|
49 |
48
|
ex |
|
50 |
3 49
|
relssdv |
|