Step |
Hyp |
Ref |
Expression |
1 |
|
odcl.1 |
|
2 |
|
odcl.2 |
|
3 |
|
odid.3 |
|
4 |
|
odid.4 |
|
5 |
|
oveq1 |
|
6 |
|
simp2l |
|
7 |
6
|
nn0zd |
|
8 |
|
simp3 |
|
9 |
7 8
|
zmodcld |
|
10 |
9
|
adantr |
|
11 |
10
|
nn0red |
|
12 |
|
simp2r |
|
13 |
12
|
nn0zd |
|
14 |
13 8
|
zmodcld |
|
15 |
14
|
adantr |
|
16 |
15
|
nn0red |
|
17 |
|
simp1l |
|
18 |
17
|
adantr |
|
19 |
|
simp1r |
|
20 |
19
|
adantr |
|
21 |
8
|
adantr |
|
22 |
6
|
nn0red |
|
23 |
8
|
nnrpd |
|
24 |
|
modlt |
|
25 |
22 23 24
|
syl2anc |
|
26 |
25
|
adantr |
|
27 |
12
|
nn0red |
|
28 |
|
modlt |
|
29 |
27 23 28
|
syl2anc |
|
30 |
29
|
adantr |
|
31 |
|
simpr |
|
32 |
1 2 3 4 18 20 21 10 15 26 30 31
|
mndodconglem |
|
33 |
31
|
eqcomd |
|
34 |
1 2 3 4 18 20 21 15 10 30 26 33
|
mndodconglem |
|
35 |
34
|
eqcomd |
|
36 |
11 16 32 35
|
lecasei |
|
37 |
36
|
ex |
|
38 |
5 37
|
impbid2 |
|
39 |
|
moddvds |
|
40 |
8 7 13 39
|
syl3anc |
|
41 |
1 2 3 4
|
odmodnn0 |
|
42 |
17 19 6 8 41
|
syl31anc |
|
43 |
1 2 3 4
|
odmodnn0 |
|
44 |
17 19 12 8 43
|
syl31anc |
|
45 |
42 44
|
eqeq12d |
|
46 |
38 40 45
|
3bitr3d |
|