Step |
Hyp |
Ref |
Expression |
1 |
|
llncvrlpln2.l |
|
2 |
|
llncvrlpln2.c |
|
3 |
|
llncvrlpln2.n |
|
4 |
|
llncvrlpln2.p |
|
5 |
|
simpr |
|
6 |
|
simpl1 |
|
7 |
|
simpl3 |
|
8 |
3 4
|
lplnnelln |
|
9 |
6 7 8
|
syl2anc |
|
10 |
|
simpl2 |
|
11 |
|
eleq1 |
|
12 |
10 11
|
syl5ibcom |
|
13 |
12
|
necon3bd |
|
14 |
9 13
|
mpd |
|
15 |
|
eqid |
|
16 |
1 15
|
pltval |
|
17 |
16
|
adantr |
|
18 |
5 14 17
|
mpbir2and |
|
19 |
|
simpl1 |
|
20 |
|
simpl2 |
|
21 |
|
eqid |
|
22 |
21 3
|
llnbase |
|
23 |
20 22
|
syl |
|
24 |
|
simpl3 |
|
25 |
21 4
|
lplnbase |
|
26 |
24 25
|
syl |
|
27 |
|
simpr |
|
28 |
|
eqid |
|
29 |
|
eqid |
|
30 |
21 1 15 28 2 29
|
hlrelat3 |
|
31 |
19 23 26 27 30
|
syl31anc |
|
32 |
21 1 28 29 4
|
islpln2 |
|
33 |
32
|
adantr |
|
34 |
|
simp3 |
|
35 |
21 28 29 3
|
islln2 |
|
36 |
|
simp3l |
|
37 |
|
simp3r |
|
38 |
|
simp12r |
|
39 |
38
|
oveq1d |
|
40 |
|
simp22 |
|
41 |
37 39 40
|
3brtr3d |
|
42 |
|
simp111 |
|
43 |
|
simp112 |
|
44 |
|
simp113 |
|
45 |
|
simp23 |
|
46 |
43 44 45
|
3jca |
|
47 |
|
simp13l |
|
48 |
|
simp13r |
|
49 |
|
simp21 |
|
50 |
47 48 49
|
3jca |
|
51 |
36 38 39
|
3brtr3d |
|
52 |
21 28 29
|
hlatjcl |
|
53 |
42 43 44 52
|
syl3anc |
|
54 |
21 1 28 2 29
|
cvr1 |
|
55 |
42 53 45 54
|
syl3anc |
|
56 |
51 55
|
mpbird |
|
57 |
|
simp12l |
|
58 |
1 28 29
|
3at |
|
59 |
42 46 50 56 57 58
|
syl32anc |
|
60 |
41 59
|
mpbid |
|
61 |
60 39 40
|
3eqtr4d |
|
62 |
36 61
|
breqtrd |
|
63 |
62
|
3exp |
|
64 |
63
|
3expd |
|
65 |
64
|
3exp |
|
66 |
65
|
3expib |
|
67 |
66
|
rexlimdvv |
|
68 |
67
|
adantld |
|
69 |
35 68
|
sylbid |
|
70 |
69
|
imp31 |
|
71 |
34 70
|
syl7 |
|
72 |
71
|
rexlimdv |
|
73 |
72
|
rexlimdvva |
|
74 |
73
|
adantld |
|
75 |
33 74
|
sylbid |
|
76 |
75
|
3impia |
|
77 |
76
|
rexlimdv |
|
78 |
77
|
imp |
|
79 |
31 78
|
syldan |
|
80 |
18 79
|
syldan |
|