Step |
Hyp |
Ref |
Expression |
1 |
|
eldifi |
|
2 |
|
limelon |
|
3 |
|
oecl |
|
4 |
1 2 3
|
syl2an |
|
5 |
|
eloni |
|
6 |
4 5
|
syl |
|
7 |
1
|
adantr |
|
8 |
2
|
adantl |
|
9 |
|
dif20el |
|
10 |
9
|
adantr |
|
11 |
|
oen0 |
|
12 |
7 8 10 11
|
syl21anc |
|
13 |
|
oelim2 |
|
14 |
1 13
|
sylan |
|
15 |
14
|
eleq2d |
|
16 |
|
eliun |
|
17 |
|
eldifi |
|
18 |
7
|
adantr |
|
19 |
8
|
adantr |
|
20 |
|
simprl |
|
21 |
|
onelon |
|
22 |
19 20 21
|
syl2anc |
|
23 |
|
oecl |
|
24 |
18 22 23
|
syl2anc |
|
25 |
|
eloni |
|
26 |
24 25
|
syl |
|
27 |
|
simprr |
|
28 |
|
ordsucss |
|
29 |
26 27 28
|
sylc |
|
30 |
|
simpll |
|
31 |
|
oeordi |
|
32 |
19 30 31
|
syl2anc |
|
33 |
20 32
|
mpd |
|
34 |
|
onelon |
|
35 |
24 27 34
|
syl2anc |
|
36 |
|
suceloni |
|
37 |
35 36
|
syl |
|
38 |
4
|
adantr |
|
39 |
|
ontr2 |
|
40 |
37 38 39
|
syl2anc |
|
41 |
29 33 40
|
mp2and |
|
42 |
41
|
expr |
|
43 |
17 42
|
sylan2 |
|
44 |
43
|
rexlimdva |
|
45 |
16 44
|
syl5bi |
|
46 |
15 45
|
sylbid |
|
47 |
46
|
ralrimiv |
|
48 |
|
dflim4 |
|
49 |
6 12 47 48
|
syl3anbrc |
|