Step |
Hyp |
Ref |
Expression |
1 |
|
gpg3kgrtriex.n |
|
2 |
|
nnre |
|
3 |
|
3rp |
|
4 |
3
|
a1i |
|
5 |
|
nnrp |
|
6 |
4 5
|
rpmulcld |
|
7 |
1 6
|
eqeltrid |
|
8 |
|
modaddmod |
|
9 |
2 2 7 8
|
syl3anc |
|
10 |
|
nncn |
|
11 |
10
|
2timesd |
|
12 |
11
|
eqcomd |
|
13 |
12
|
oveq1d |
|
14 |
|
2cnd |
|
15 |
14 10
|
adddirp1d |
|
16 |
|
2p1e3 |
|
17 |
16
|
oveq1i |
|
18 |
15 17
|
eqtr3di |
|
19 |
18
|
oveq1d |
|
20 |
1
|
a1i |
|
21 |
20
|
oveq2d |
|
22 |
|
modid0 |
|
23 |
6 22
|
syl |
|
24 |
19 21 23
|
3eqtrd |
|
25 |
|
2nn |
|
26 |
25
|
a1i |
|
27 |
|
id |
|
28 |
26 27
|
nnmulcld |
|
29 |
28
|
nnzd |
|
30 |
|
nnz |
|
31 |
|
3nn |
|
32 |
31
|
a1i |
|
33 |
32 27
|
nnmulcld |
|
34 |
1 33
|
eqeltrid |
|
35 |
|
summodnegmod |
|
36 |
29 30 34 35
|
syl3anc |
|
37 |
24 36
|
mpbid |
|
38 |
9 13 37
|
3eqtrrd |
|