Step |
Hyp |
Ref |
Expression |
1 |
|
distop |
|
2 |
|
distop |
|
3 |
|
unipw |
|
4 |
3
|
eqcomi |
|
5 |
|
unipw |
|
6 |
5
|
eqcomi |
|
7 |
4 6
|
txuni |
|
8 |
1 2 7
|
syl2an |
|
9 |
|
eqimss2 |
|
10 |
8 9
|
syl |
|
11 |
|
sspwuni |
|
12 |
10 11
|
sylibr |
|
13 |
|
elelpwi |
|
14 |
13
|
adantl |
|
15 |
|
xp1st |
|
16 |
|
snelpwi |
|
17 |
14 15 16
|
3syl |
|
18 |
|
xp2nd |
|
19 |
|
snelpwi |
|
20 |
14 18 19
|
3syl |
|
21 |
|
vsnid |
|
22 |
|
1st2nd2 |
|
23 |
14 22
|
syl |
|
24 |
23
|
sneqd |
|
25 |
21 24
|
eleqtrid |
|
26 |
|
simprl |
|
27 |
23 26
|
eqeltrrd |
|
28 |
27
|
snssd |
|
29 |
|
xpeq1 |
|
30 |
29
|
eleq2d |
|
31 |
29
|
sseq1d |
|
32 |
30 31
|
anbi12d |
|
33 |
|
xpeq2 |
|
34 |
|
fvex |
|
35 |
|
fvex |
|
36 |
34 35
|
xpsn |
|
37 |
33 36
|
eqtrdi |
|
38 |
37
|
eleq2d |
|
39 |
37
|
sseq1d |
|
40 |
38 39
|
anbi12d |
|
41 |
32 40
|
rspc2ev |
|
42 |
17 20 25 28 41
|
syl112anc |
|
43 |
42
|
expr |
|
44 |
43
|
ralrimdva |
|
45 |
|
eltx |
|
46 |
1 2 45
|
syl2an |
|
47 |
44 46
|
sylibrd |
|
48 |
47
|
ssrdv |
|
49 |
12 48
|
eqssd |
|