Step |
Hyp |
Ref |
Expression |
1 |
|
fpprbasnn |
|
2 |
|
fpprel |
|
3 |
|
3simpa |
|
4 |
3
|
a1i |
|
5 |
2 4
|
sylbid |
|
6 |
1 5
|
mpcom |
|
7 |
|
fpprwppr |
|
8 |
1 7
|
jca |
|
9 |
6 8
|
jca |
|
10 |
|
simprll |
|
11 |
|
simprlr |
|
12 |
|
eluz4nn |
|
13 |
12
|
adantr |
|
14 |
|
nnz |
|
15 |
12
|
nnnn0d |
|
16 |
|
zexpcl |
|
17 |
14 15 16
|
syl2anr |
|
18 |
14
|
adantl |
|
19 |
|
moddvds |
|
20 |
13 17 18 19
|
syl3anc |
|
21 |
|
nncn |
|
22 |
|
expm1t |
|
23 |
21 12 22
|
syl2anr |
|
24 |
23
|
oveq1d |
|
25 |
|
nnm1nn0 |
|
26 |
12 25
|
syl |
|
27 |
|
zexpcl |
|
28 |
14 26 27
|
syl2anr |
|
29 |
28
|
zcnd |
|
30 |
21
|
adantl |
|
31 |
29 30
|
mulsubfacd |
|
32 |
24 31
|
eqtrd |
|
33 |
32
|
breq2d |
|
34 |
|
1zzd |
|
35 |
28 34
|
zsubcld |
|
36 |
|
dvdsmulgcd |
|
37 |
35 18 36
|
syl2anc |
|
38 |
|
eluzelz |
|
39 |
|
gcdcom |
|
40 |
38 14 39
|
syl2an |
|
41 |
40
|
eqeq1d |
|
42 |
41
|
biimpd |
|
43 |
42
|
imp |
|
44 |
43
|
oveq2d |
|
45 |
35
|
zcnd |
|
46 |
45
|
mulid1d |
|
47 |
46
|
adantr |
|
48 |
44 47
|
eqtrd |
|
49 |
48
|
breq2d |
|
50 |
49
|
biimpd |
|
51 |
50
|
ex |
|
52 |
51
|
com23 |
|
53 |
37 52
|
sylbid |
|
54 |
33 53
|
sylbid |
|
55 |
20 54
|
sylbid |
|
56 |
55
|
expimpd |
|
57 |
56
|
adantr |
|
58 |
57
|
imp |
|
59 |
58
|
impcom |
|
60 |
|
eluz4eluz2 |
|
61 |
60
|
adantr |
|
62 |
61
|
adantr |
|
63 |
14
|
adantr |
|
64 |
26
|
adantr |
|
65 |
63 64 27
|
syl2anr |
|
66 |
62 65
|
jca |
|
67 |
66
|
adantl |
|
68 |
|
modm1div |
|
69 |
67 68
|
syl |
|
70 |
59 69
|
mpbird |
|
71 |
2
|
adantr |
|
72 |
71
|
adantl |
|
73 |
72
|
adantl |
|
74 |
10 11 70 73
|
mpbir3and |
|
75 |
74
|
ex |
|
76 |
9 75
|
impbid2 |
|