Step |
Hyp |
Ref |
Expression |
1 |
|
metidss |
|
2 |
|
xpss |
|
3 |
1 2
|
sstrdi |
|
4 |
|
df-rel |
|
5 |
3 4
|
sylibr |
|
6 |
1
|
ssbrd |
|
7 |
6
|
imp |
|
8 |
|
brxp |
|
9 |
7 8
|
sylib |
|
10 |
|
psmetsym |
|
11 |
10
|
3expb |
|
12 |
11
|
eqeq1d |
|
13 |
|
metidv |
|
14 |
|
metidv |
|
15 |
14
|
ancom2s |
|
16 |
12 13 15
|
3bitr4d |
|
17 |
16
|
biimpd |
|
18 |
17
|
impancom |
|
19 |
9 18
|
mpd |
|
20 |
|
simpl |
|
21 |
|
simprr |
|
22 |
1
|
ssbrd |
|
23 |
22
|
imp |
|
24 |
|
brxp |
|
25 |
23 24
|
sylib |
|
26 |
21 25
|
syldan |
|
27 |
26
|
simpld |
|
28 |
|
simprl |
|
29 |
28 9
|
syldan |
|
30 |
29
|
simpld |
|
31 |
26
|
simprd |
|
32 |
|
psmettri2 |
|
33 |
20 27 30 31 32
|
syl13anc |
|
34 |
29 11
|
syldan |
|
35 |
29 13
|
syldan |
|
36 |
28 35
|
mpbid |
|
37 |
34 36
|
eqtr3d |
|
38 |
|
metidv |
|
39 |
26 38
|
syldan |
|
40 |
21 39
|
mpbid |
|
41 |
37 40
|
oveq12d |
|
42 |
|
0xr |
|
43 |
|
xaddid1 |
|
44 |
42 43
|
ax-mp |
|
45 |
41 44
|
eqtrdi |
|
46 |
33 45
|
breqtrd |
|
47 |
|
psmetge0 |
|
48 |
20 30 31 47
|
syl3anc |
|
49 |
|
psmetcl |
|
50 |
20 30 31 49
|
syl3anc |
|
51 |
|
xrletri3 |
|
52 |
50 42 51
|
sylancl |
|
53 |
46 48 52
|
mpbir2and |
|
54 |
|
metidv |
|
55 |
20 30 31 54
|
syl12anc |
|
56 |
53 55
|
mpbird |
|
57 |
|
psmet0 |
|
58 |
|
metidv |
|
59 |
58
|
anabsan2 |
|
60 |
57 59
|
mpbird |
|
61 |
1
|
ssbrd |
|
62 |
61
|
imp |
|
63 |
|
brxp |
|
64 |
62 63
|
sylib |
|
65 |
64
|
simpld |
|
66 |
60 65
|
impbida |
|
67 |
5 19 56 66
|
iserd |
|