Step |
Hyp |
Ref |
Expression |
1 |
|
2dvdseven |
|
2 |
1
|
ad2antlr |
|
3 |
|
2prm |
|
4 |
|
simpll |
|
5 |
|
pcelnn |
|
6 |
3 4 5
|
sylancr |
|
7 |
2 6
|
mpbird |
|
8 |
7
|
nnzd |
|
9 |
8
|
peano2zd |
|
10 |
|
pcdvds |
|
11 |
3 4 10
|
sylancr |
|
12 |
|
2nn |
|
13 |
7
|
nnnn0d |
|
14 |
|
nnexpcl |
|
15 |
12 13 14
|
sylancr |
|
16 |
|
nndivdvds |
|
17 |
4 15 16
|
syl2anc |
|
18 |
11 17
|
mpbid |
|
19 |
18
|
nnzd |
|
20 |
|
pcndvds2 |
|
21 |
3 4 20
|
sylancr |
|
22 |
|
isodd3 |
|
23 |
19 21 22
|
sylanbrc |
|
24 |
|
simpr |
|
25 |
|
nncn |
|
26 |
25
|
ad2antrr |
|
27 |
15
|
nncnd |
|
28 |
15
|
nnne0d |
|
29 |
26 27 28
|
divcan2d |
|
30 |
29
|
oveq2d |
|
31 |
29
|
oveq2d |
|
32 |
24 30 31
|
3eqtr4d |
|
33 |
7 18 23 32
|
perfectALTVlem2 |
|
34 |
33
|
simprd |
|
35 |
33
|
simpld |
|
36 |
34 35
|
eqeltrrd |
|
37 |
7
|
nncnd |
|
38 |
|
ax-1cn |
|
39 |
|
pncan |
|
40 |
37 38 39
|
sylancl |
|
41 |
40
|
eqcomd |
|
42 |
41
|
oveq2d |
|
43 |
42 34
|
oveq12d |
|
44 |
29 43
|
eqtr3d |
|
45 |
|
oveq2 |
|
46 |
45
|
oveq1d |
|
47 |
46
|
eleq1d |
|
48 |
|
oveq1 |
|
49 |
48
|
oveq2d |
|
50 |
49 46
|
oveq12d |
|
51 |
50
|
eqeq2d |
|
52 |
47 51
|
anbi12d |
|
53 |
52
|
rspcev |
|
54 |
9 36 44 53
|
syl12anc |
|
55 |
54
|
ex |
|
56 |
|
perfect1 |
|
57 |
|
2cn |
|
58 |
|
mersenne |
|
59 |
|
prmnn |
|
60 |
58 59
|
syl |
|
61 |
|
expm1t |
|
62 |
57 60 61
|
sylancr |
|
63 |
|
nnm1nn0 |
|
64 |
60 63
|
syl |
|
65 |
|
expcl |
|
66 |
57 64 65
|
sylancr |
|
67 |
|
mulcom |
|
68 |
66 57 67
|
sylancl |
|
69 |
62 68
|
eqtrd |
|
70 |
69
|
oveq1d |
|
71 |
|
2cnd |
|
72 |
|
prmnn |
|
73 |
72
|
adantl |
|
74 |
73
|
nncnd |
|
75 |
71 66 74
|
mulassd |
|
76 |
56 70 75
|
3eqtrd |
|
77 |
|
oveq2 |
|
78 |
|
oveq2 |
|
79 |
77 78
|
eqeq12d |
|
80 |
76 79
|
syl5ibrcom |
|
81 |
80
|
impr |
|
82 |
81
|
rexlimiva |
|
83 |
55 82
|
impbid1 |
|