Step |
Hyp |
Ref |
Expression |
1 |
|
2lnat.b |
|
2 |
|
2lnat.m |
|
3 |
|
2lnat.z |
|
4 |
|
2lnat.a |
|
5 |
|
2lnat.n |
|
6 |
|
2lnat.f |
|
7 |
|
simp11 |
|
8 |
|
hlatl |
|
9 |
7 8
|
syl |
|
10 |
7
|
hllatd |
|
11 |
|
simp12 |
|
12 |
|
simp13 |
|
13 |
1 2
|
latmcl |
|
14 |
10 11 12 13
|
syl3anc |
|
15 |
|
simp3r |
|
16 |
|
eqid |
|
17 |
1 16 3 4
|
atlex |
|
18 |
9 14 15 17
|
syl3anc |
|
19 |
|
simp13l |
|
20 |
|
simp11 |
|
21 |
|
simp12l |
|
22 |
|
simp12r |
|
23 |
1 16 5 6
|
lncmp |
|
24 |
20 21 22 23
|
syl12anc |
|
25 |
|
simp111 |
|
26 |
25
|
hllatd |
|
27 |
|
simp112 |
|
28 |
|
simp113 |
|
29 |
1 16 2
|
latleeqm1 |
|
30 |
26 27 28 29
|
syl3anc |
|
31 |
24 30
|
bitr3d |
|
32 |
31
|
necon3bid |
|
33 |
19 32
|
mpbid |
|
34 |
|
simp3 |
|
35 |
1 16 2
|
latmle1 |
|
36 |
26 27 28 35
|
syl3anc |
|
37 |
|
hlpos |
|
38 |
25 37
|
syl |
|
39 |
1 4
|
atbase |
|
40 |
39
|
3ad2ant2 |
|
41 |
26 27 28 13
|
syl3anc |
|
42 |
|
simp2 |
|
43 |
1 16 26 40 41 27 34 36
|
lattrd |
|
44 |
|
eqid |
|
45 |
1 16 44 4 5 6
|
lncvrat |
|
46 |
25 27 42 21 43 45
|
syl32anc |
|
47 |
1 16 44
|
cvrnbtwn4 |
|
48 |
38 40 27 41 46 47
|
syl131anc |
|
49 |
34 36 48
|
mpbi2and |
|
50 |
|
neor |
|
51 |
49 50
|
sylib |
|
52 |
51
|
necon1d |
|
53 |
33 52
|
mpd |
|
54 |
53
|
3exp |
|
55 |
54
|
reximdvai |
|
56 |
18 55
|
mpd |
|
57 |
|
risset |
|
58 |
56 57
|
sylibr |
|