Step |
Hyp |
Ref |
Expression |
1 |
|
osumcl.p |
|
2 |
|
osumcl.o |
|
3 |
|
osumcl.c |
|
4 |
|
nonconne |
|
5 |
|
simpl1 |
|
6 |
|
simpl2 |
|
7 |
|
eqid |
|
8 |
7 3
|
psubclssatN |
|
9 |
5 6 8
|
syl2anc |
|
10 |
|
simpl3 |
|
11 |
7 3
|
psubclssatN |
|
12 |
5 10 11
|
syl2anc |
|
13 |
7 1
|
paddssat |
|
14 |
5 9 12 13
|
syl3anc |
|
15 |
7 2
|
2polssN |
|
16 |
5 14 15
|
syl2anc |
|
17 |
|
df-pss |
|
18 |
|
pssnel |
|
19 |
17 18
|
sylbir |
|
20 |
|
df-rex |
|
21 |
19 20
|
sylibr |
|
22 |
|
eqid |
|
23 |
|
eqid |
|
24 |
|
eqid |
|
25 |
|
eqid |
|
26 |
22 23 7 1 2 3 24 25
|
osumcllem9N |
|
27 |
|
simp11 |
|
28 |
|
simp12 |
|
29 |
27 28 8
|
syl2anc |
|
30 |
|
simp13 |
|
31 |
27 30 11
|
syl2anc |
|
32 |
14
|
3adantr3 |
|
33 |
32
|
3adant3 |
|
34 |
7 2
|
polssatN |
|
35 |
27 33 34
|
syl2anc |
|
36 |
7 2
|
polssatN |
|
37 |
27 35 36
|
syl2anc |
|
38 |
|
simp23 |
|
39 |
37 38
|
sseldd |
|
40 |
|
simp3 |
|
41 |
22 23 7 1 2 3 24 25
|
osumcllem10N |
|
42 |
27 29 31 39 40 41
|
syl311anc |
|
43 |
26 42
|
pm2.21ddne |
|
44 |
43
|
3exp |
|
45 |
44
|
3expd |
|
46 |
45
|
imp32 |
|
47 |
46
|
rexlimdv |
|
48 |
21 47
|
syl5 |
|
49 |
16 48
|
mpand |
|
50 |
49
|
necon1bd |
|
51 |
4 50
|
mpi |
|