Step |
Hyp |
Ref |
Expression |
1 |
|
mersenne |
|
2 |
|
prmnn |
|
3 |
1 2
|
syl |
|
4 |
|
1sgm2ppw |
|
5 |
3 4
|
syl |
|
6 |
|
1sgmprm |
|
7 |
6
|
adantl |
|
8 |
|
2nn |
|
9 |
3
|
nnnn0d |
|
10 |
|
nnexpcl |
|
11 |
8 9 10
|
sylancr |
|
12 |
11
|
nncnd |
|
13 |
|
ax-1cn |
|
14 |
|
npcan |
|
15 |
12 13 14
|
sylancl |
|
16 |
7 15
|
eqtrd |
|
17 |
5 16
|
oveq12d |
|
18 |
13
|
a1i |
|
19 |
|
nnm1nn0 |
|
20 |
3 19
|
syl |
|
21 |
|
nnexpcl |
|
22 |
8 20 21
|
sylancr |
|
23 |
|
prmnn |
|
24 |
23
|
adantl |
|
25 |
22
|
nnzd |
|
26 |
|
prmz |
|
27 |
26
|
adantl |
|
28 |
25 27
|
gcdcomd |
|
29 |
|
iddvds |
|
30 |
27 29
|
syl |
|
31 |
|
prmuz2 |
|
32 |
31
|
adantl |
|
33 |
|
eluz2gt1 |
|
34 |
32 33
|
syl |
|
35 |
|
ndvdsp1 |
|
36 |
27 24 34 35
|
syl3anc |
|
37 |
30 36
|
mpd |
|
38 |
|
2z |
|
39 |
38
|
a1i |
|
40 |
|
dvdsmultr1 |
|
41 |
27 25 39 40
|
syl3anc |
|
42 |
|
2cn |
|
43 |
|
expm1t |
|
44 |
42 3 43
|
sylancr |
|
45 |
15 44
|
eqtr2d |
|
46 |
45
|
breq2d |
|
47 |
41 46
|
sylibd |
|
48 |
37 47
|
mtod |
|
49 |
|
simpr |
|
50 |
|
coprm |
|
51 |
49 25 50
|
syl2anc |
|
52 |
48 51
|
mpbid |
|
53 |
28 52
|
eqtrd |
|
54 |
|
sgmmul |
|
55 |
18 22 24 53 54
|
syl13anc |
|
56 |
|
subcl |
|
57 |
12 13 56
|
sylancl |
|
58 |
12 57
|
mulcomd |
|
59 |
17 55 58
|
3eqtr4d |
|