Step |
Hyp |
Ref |
Expression |
1 |
|
pl42lem.b |
|
2 |
|
pl42lem.l |
|
3 |
|
pl42lem.j |
|
4 |
|
pl42lem.m |
|
5 |
|
pl42lem.o |
|
6 |
|
pl42lem.f |
|
7 |
|
pl42lem.p |
|
8 |
1 2 3 4 5 6 7
|
pl42lem1N |
|
9 |
8
|
3impia |
|
10 |
1 2 3 4 5 6 7
|
pl42lem3N |
|
11 |
|
simpl1 |
|
12 |
11
|
hllatd |
|
13 |
|
simpl2 |
|
14 |
|
eqid |
|
15 |
1 14 6
|
pmapsub |
|
16 |
12 13 15
|
syl2anc |
|
17 |
|
simpl3 |
|
18 |
1 14 6
|
pmapsub |
|
19 |
12 17 18
|
syl2anc |
|
20 |
|
simpr2 |
|
21 |
1 14 6
|
pmapsub |
|
22 |
12 20 21
|
syl2anc |
|
23 |
|
simpr3 |
|
24 |
1 14 6
|
pmapsub |
|
25 |
12 23 24
|
syl2anc |
|
26 |
14 7
|
pmodl42N |
|
27 |
11 16 19 22 25 26
|
syl32anc |
|
28 |
1 2 3 4 5 6 7
|
pl42lem2N |
|
29 |
27 28
|
eqsstrd |
|
30 |
10 29
|
sstrd |
|
31 |
30
|
3adant3 |
|
32 |
9 31
|
eqsstrd |
|
33 |
32
|
3expia |
|