Step |
Hyp |
Ref |
Expression |
1 |
|
9nn |
|
2 |
1
|
elexi |
|
3 |
|
eleq1 |
|
4 |
|
oveq2 |
|
5 |
|
id |
|
6 |
4 5
|
oveq12d |
|
7 |
|
oveq2 |
|
8 |
6 7
|
eqeq12d |
|
9 |
|
eleq1 |
|
10 |
8 9
|
imbi12d |
|
11 |
10
|
notbid |
|
12 |
3 11
|
anbi12d |
|
13 |
|
3z |
|
14 |
1
|
nnzi |
|
15 |
|
3re |
|
16 |
|
9re |
|
17 |
|
3lt9 |
|
18 |
15 16 17
|
ltleii |
|
19 |
|
eluz2 |
|
20 |
13 14 18 19
|
mpbir3an |
|
21 |
|
8nn |
|
22 |
|
8nn0 |
|
23 |
|
0z |
|
24 |
|
1nn0 |
|
25 |
|
8exp8mod9 |
|
26 |
|
1re |
|
27 |
|
nnrp |
|
28 |
1 27
|
ax-mp |
|
29 |
|
0le1 |
|
30 |
|
1lt9 |
|
31 |
|
modid |
|
32 |
26 28 29 30 31
|
mp4an |
|
33 |
25 32
|
eqtr4i |
|
34 |
|
8p1e9 |
|
35 |
|
8cn |
|
36 |
35
|
addid2i |
|
37 |
|
9cn |
|
38 |
37
|
mul02i |
|
39 |
38
|
oveq1i |
|
40 |
35
|
mulid2i |
|
41 |
36 39 40
|
3eqtr4i |
|
42 |
1 21 22 23 24 22 33 34 41
|
modxp1i |
|
43 |
|
9nprm |
|
44 |
42 43
|
pm3.2i |
|
45 |
|
annim |
|
46 |
44 45
|
mpbi |
|
47 |
20 46
|
pm3.2i |
|
48 |
2 12 47
|
ceqsexv2d |
|
49 |
|
df-rex |
|
50 |
48 49
|
mpbir |
|