Step |
Hyp |
Ref |
Expression |
1 |
|
lplncmp.l |
|
2 |
|
lplncmp.p |
|
3 |
|
simp2 |
|
4 |
|
simp1 |
|
5 |
|
eqid |
|
6 |
5 2
|
lplnbase |
|
7 |
6
|
3ad2ant2 |
|
8 |
|
eqid |
|
9 |
|
eqid |
|
10 |
5 8 9 2
|
islpln4 |
|
11 |
4 7 10
|
syl2anc |
|
12 |
3 11
|
mpbid |
|
13 |
|
simpr3 |
|
14 |
|
hlpos |
|
15 |
14
|
3ad2ant1 |
|
16 |
15
|
adantr |
|
17 |
7
|
adantr |
|
18 |
|
simpl3 |
|
19 |
5 2
|
lplnbase |
|
20 |
18 19
|
syl |
|
21 |
|
simpr1 |
|
22 |
5 9
|
llnbase |
|
23 |
21 22
|
syl |
|
24 |
|
simpr2 |
|
25 |
|
simpl1 |
|
26 |
5 1 8
|
cvrle |
|
27 |
25 23 17 24 26
|
syl31anc |
|
28 |
5 1
|
postr |
|
29 |
16 23 17 20 28
|
syl13anc |
|
30 |
27 13 29
|
mp2and |
|
31 |
1 8 9 2
|
llncvrlpln2 |
|
32 |
25 21 18 30 31
|
syl31anc |
|
33 |
5 1 8
|
cvrcmp |
|
34 |
16 17 20 23 24 32 33
|
syl132anc |
|
35 |
13 34
|
mpbid |
|
36 |
35
|
3exp2 |
|
37 |
36
|
rexlimdv |
|
38 |
12 37
|
mpd |
|
39 |
5 1
|
posref |
|
40 |
15 7 39
|
syl2anc |
|
41 |
|
breq2 |
|
42 |
40 41
|
syl5ibcom |
|
43 |
38 42
|
impbid |
|