Step |
Hyp |
Ref |
Expression |
1 |
|
2llnj.l |
|
2 |
|
2llnj.j |
|
3 |
|
2llnj.n |
|
4 |
|
2llnj.p |
|
5 |
|
eqid |
|
6 |
|
eqid |
|
7 |
5 2 6 3
|
islln2 |
|
8 |
|
simpr |
|
9 |
7 8
|
syl6bi |
|
10 |
5 2 6 3
|
islln2 |
|
11 |
|
simpr |
|
12 |
10 11
|
syl6bi |
|
13 |
9 12
|
anim12d |
|
14 |
13
|
imp |
|
15 |
14
|
3adantr3 |
|
16 |
15
|
3adant3 |
|
17 |
|
simp2rr |
|
18 |
|
simp3rr |
|
19 |
17 18
|
oveq12d |
|
20 |
|
simp13 |
|
21 |
|
breq1 |
|
22 |
|
neeq1 |
|
23 |
21 22
|
3anbi13d |
|
24 |
|
breq1 |
|
25 |
|
neeq2 |
|
26 |
24 25
|
3anbi23d |
|
27 |
23 26
|
sylan9bb |
|
28 |
17 18 27
|
syl2anc |
|
29 |
20 28
|
mpbid |
|
30 |
|
simp11 |
|
31 |
|
simp123 |
|
32 |
|
simp2ll |
|
33 |
|
simp2lr |
|
34 |
|
simp2rl |
|
35 |
|
simp3ll |
|
36 |
|
simp3lr |
|
37 |
|
simp3rl |
|
38 |
1 2 6 3 4
|
2llnjaN |
|
39 |
38
|
ex |
|
40 |
30 31 32 33 34 35 36 37 39
|
syl233anc |
|
41 |
29 40
|
mpd |
|
42 |
19 41
|
eqtrd |
|
43 |
42
|
3exp |
|
44 |
43
|
3impib |
|
45 |
44
|
expd |
|
46 |
45
|
rexlimdvv |
|
47 |
46
|
3exp |
|
48 |
47
|
rexlimdvv |
|
49 |
48
|
impd |
|
50 |
16 49
|
mpd |
|