Step |
Hyp |
Ref |
Expression |
1 |
|
pmapojoin.b |
|
2 |
|
pmapojoin.l |
|
3 |
|
pmapojoin.j |
|
4 |
|
pmapojoin.m |
|
5 |
|
pmapojoin.o |
|
6 |
|
pmapojoin.p |
|
7 |
|
eqid |
|
8 |
1 3 4 6 7
|
pmapj2N |
|
9 |
8
|
adantr |
|
10 |
|
simpl1 |
|
11 |
|
simpl2 |
|
12 |
|
eqid |
|
13 |
1 4 12
|
pmapsubclN |
|
14 |
10 11 13
|
syl2anc |
|
15 |
|
simpl3 |
|
16 |
1 4 12
|
pmapsubclN |
|
17 |
10 15 16
|
syl2anc |
|
18 |
|
hlop |
|
19 |
18
|
3ad2ant1 |
|
20 |
|
simp3 |
|
21 |
1 5
|
opoccl |
|
22 |
19 20 21
|
syl2anc |
|
23 |
1 2 4
|
pmaple |
|
24 |
22 23
|
syld3an3 |
|
25 |
24
|
biimpa |
|
26 |
1 5 4 7
|
polpmapN |
|
27 |
10 15 26
|
syl2anc |
|
28 |
25 27
|
sseqtrrd |
|
29 |
6 7 12
|
osumclN |
|
30 |
10 14 17 28 29
|
syl31anc |
|
31 |
7 12
|
psubcli2N |
|
32 |
10 30 31
|
syl2anc |
|
33 |
9 32
|
eqtrd |
|