Step |
Hyp |
Ref |
Expression |
1 |
|
sltlpss |
|
2 |
|
fveq2 |
|
3 |
|
simpr |
|
4 |
|
lruneq |
|
5 |
4
|
adantr |
|
6 |
5 3
|
difeq12d |
|
7 |
|
difundir |
|
8 |
|
difid |
|
9 |
8
|
uneq1i |
|
10 |
|
0un |
|
11 |
7 9 10
|
3eqtri |
|
12 |
|
incom |
|
13 |
|
lltropt |
|
14 |
|
ssltdisj |
|
15 |
13 14
|
mp1i |
|
16 |
12 15
|
eqtr3id |
|
17 |
|
disjdif2 |
|
18 |
16 17
|
syl |
|
19 |
11 18
|
eqtrid |
|
20 |
|
difundir |
|
21 |
|
difid |
|
22 |
21
|
uneq1i |
|
23 |
|
0un |
|
24 |
20 22 23
|
3eqtri |
|
25 |
|
incom |
|
26 |
|
lltropt |
|
27 |
|
ssltdisj |
|
28 |
26 27
|
mp1i |
|
29 |
25 28
|
eqtr3id |
|
30 |
|
disjdif2 |
|
31 |
29 30
|
syl |
|
32 |
24 31
|
eqtrid |
|
33 |
6 19 32
|
3eqtr3d |
|
34 |
3 33
|
oveq12d |
|
35 |
|
simpl1 |
|
36 |
|
lrcut |
|
37 |
35 36
|
syl |
|
38 |
|
simpl2 |
|
39 |
|
lrcut |
|
40 |
38 39
|
syl |
|
41 |
34 37 40
|
3eqtr3d |
|
42 |
41
|
ex |
|
43 |
2 42
|
impbid2 |
|
44 |
1 43
|
orbi12d |
|
45 |
|
sleloe |
|
46 |
45
|
3adant3 |
|
47 |
|
sspss |
|
48 |
47
|
a1i |
|
49 |
44 46 48
|
3bitr4d |
|