Step |
Hyp |
Ref |
Expression |
1 |
|
llnexch.l |
|
2 |
|
llnexch.j |
|
3 |
|
llnexch.m |
|
4 |
|
llnexch.a |
|
5 |
|
llnexch.n |
|
6 |
|
simp23 |
|
7 |
|
simp1 |
|
8 |
|
eqid |
|
9 |
8 5
|
llnbase |
|
10 |
6 9
|
syl |
|
11 |
8 2 4 5
|
islln3 |
|
12 |
7 10 11
|
syl2anc |
|
13 |
6 12
|
mpbid |
|
14 |
|
simp3r |
|
15 |
14
|
necomd |
|
16 |
|
simp11 |
|
17 |
16
|
hllatd |
|
18 |
|
simp2l |
|
19 |
8 4
|
atbase |
|
20 |
18 19
|
syl |
|
21 |
|
simp2r |
|
22 |
8 4
|
atbase |
|
23 |
21 22
|
syl |
|
24 |
|
simp121 |
|
25 |
8 5
|
llnbase |
|
26 |
24 25
|
syl |
|
27 |
8 1 2
|
latjle12 |
|
28 |
17 20 23 26 27
|
syl13anc |
|
29 |
|
simp3 |
|
30 |
2 4 5
|
llni2 |
|
31 |
16 18 21 29 30
|
syl31anc |
|
32 |
1 5
|
llncmp |
|
33 |
16 31 24 32
|
syl3anc |
|
34 |
28 33
|
bitr2d |
|
35 |
34
|
necon3abid |
|
36 |
|
ianor |
|
37 |
35 36
|
bitrdi |
|
38 |
|
simpl11 |
|
39 |
24
|
adantr |
|
40 |
|
simp122 |
|
41 |
40
|
adantr |
|
42 |
|
simpl2l |
|
43 |
|
simpl2r |
|
44 |
|
simpr |
|
45 |
|
simp13l |
|
46 |
45
|
adantr |
|
47 |
1 2 3 4 5
|
llnexchb2lem |
|
48 |
38 39 41 42 43 44 46 47
|
syl331anc |
|
49 |
48
|
ex |
|
50 |
|
simpl11 |
|
51 |
24
|
adantr |
|
52 |
40
|
adantr |
|
53 |
|
simpl2r |
|
54 |
|
simpl2l |
|
55 |
|
simpr |
|
56 |
45
|
adantr |
|
57 |
1 2 3 4 5
|
llnexchb2lem |
|
58 |
50 51 52 53 54 55 56 57
|
syl331anc |
|
59 |
2 4
|
hlatjcom |
|
60 |
50 54 53 59
|
syl3anc |
|
61 |
60
|
breq2d |
|
62 |
60
|
oveq2d |
|
63 |
62
|
eqeq2d |
|
64 |
58 61 63
|
3bitr4d |
|
65 |
64
|
ex |
|
66 |
49 65
|
jaod |
|
67 |
37 66
|
sylbid |
|
68 |
|
neeq1 |
|
69 |
|
breq2 |
|
70 |
|
oveq2 |
|
71 |
70
|
eqeq2d |
|
72 |
69 71
|
bibi12d |
|
73 |
68 72
|
imbi12d |
|
74 |
67 73
|
syl5ibrcom |
|
75 |
74
|
3exp |
|
76 |
75
|
imp4a |
|
77 |
76
|
rexlimdvv |
|
78 |
13 15 77
|
mp2d |
|