Step |
Hyp |
Ref |
Expression |
1 |
|
llnle.b |
|
2 |
|
llnle.l |
|
3 |
|
llnle.z |
|
4 |
|
llnle.a |
|
5 |
|
llnle.n |
|
6 |
|
simpll |
|
7 |
|
simplr |
|
8 |
|
simprl |
|
9 |
1 2 3 4
|
atle |
|
10 |
6 7 8 9
|
syl3anc |
|
11 |
|
simp1ll |
|
12 |
1 4
|
atbase |
|
13 |
12
|
3ad2ant2 |
|
14 |
|
simp1lr |
|
15 |
|
simp3 |
|
16 |
|
simp2 |
|
17 |
|
simp1rr |
|
18 |
|
nelne2 |
|
19 |
16 17 18
|
syl2anc |
|
20 |
|
eqid |
|
21 |
2 20
|
pltval |
|
22 |
11 16 14 21
|
syl3anc |
|
23 |
15 19 22
|
mpbir2and |
|
24 |
|
eqid |
|
25 |
|
eqid |
|
26 |
1 2 20 24 25 4
|
hlrelat3 |
|
27 |
11 13 14 23 26
|
syl31anc |
|
28 |
|
simp1ll |
|
29 |
|
simp21 |
|
30 |
|
simp23 |
|
31 |
1 24 4
|
hlatjcl |
|
32 |
28 29 30 31
|
syl3anc |
|
33 |
|
simp3l |
|
34 |
1 25 4 5
|
llni |
|
35 |
28 32 29 33 34
|
syl31anc |
|
36 |
|
simp3r |
|
37 |
|
breq1 |
|
38 |
37
|
rspcev |
|
39 |
35 36 38
|
syl2anc |
|
40 |
39
|
3exp |
|
41 |
40
|
3expd |
|
42 |
41
|
3imp |
|
43 |
42
|
rexlimdv |
|
44 |
27 43
|
mpd |
|
45 |
44
|
3exp |
|
46 |
45
|
rexlimdv |
|
47 |
10 46
|
mpd |
|