Step |
Hyp |
Ref |
Expression |
1 |
|
odmulgid.1 |
|
2 |
|
odmulgid.2 |
|
3 |
|
odmulgid.3 |
|
4 |
|
simpl3 |
|
5 |
|
simpl2 |
|
6 |
1 2
|
odcl |
|
7 |
5 6
|
syl |
|
8 |
7
|
nn0zd |
|
9 |
|
bezout |
|
10 |
4 8 9
|
syl2anc |
|
11 |
|
oveq1 |
|
12 |
11
|
eqcoms |
|
13 |
|
simpll1 |
|
14 |
4
|
adantr |
|
15 |
|
simprl |
|
16 |
14 15
|
zmulcld |
|
17 |
5
|
adantr |
|
18 |
17 6
|
syl |
|
19 |
18
|
nn0zd |
|
20 |
|
simprr |
|
21 |
19 20
|
zmulcld |
|
22 |
|
eqid |
|
23 |
1 3 22
|
mulgdir |
|
24 |
13 16 21 17 23
|
syl13anc |
|
25 |
14
|
zcnd |
|
26 |
15
|
zcnd |
|
27 |
25 26
|
mulcomd |
|
28 |
27
|
oveq1d |
|
29 |
1 3
|
mulgass |
|
30 |
13 15 14 17 29
|
syl13anc |
|
31 |
28 30
|
eqtrd |
|
32 |
|
dvdsmul1 |
|
33 |
19 20 32
|
syl2anc |
|
34 |
|
eqid |
|
35 |
1 2 3 34
|
oddvds |
|
36 |
13 17 21 35
|
syl3anc |
|
37 |
33 36
|
mpbid |
|
38 |
31 37
|
oveq12d |
|
39 |
1 3
|
mulgcl |
|
40 |
13 14 17 39
|
syl3anc |
|
41 |
1 3
|
mulgcl |
|
42 |
13 15 40 41
|
syl3anc |
|
43 |
1 22 34
|
grprid |
|
44 |
13 42 43
|
syl2anc |
|
45 |
38 44
|
eqtrd |
|
46 |
24 45
|
eqtrd |
|
47 |
|
simplr |
|
48 |
47
|
oveq1d |
|
49 |
1 3
|
mulg1 |
|
50 |
17 49
|
syl |
|
51 |
48 50
|
eqtrd |
|
52 |
46 51
|
eqeq12d |
|
53 |
12 52
|
syl5ib |
|
54 |
53
|
anassrs |
|
55 |
54
|
rexlimdva |
|
56 |
55
|
reximdva |
|
57 |
10 56
|
mpd |
|