Step |
Hyp |
Ref |
Expression |
1 |
|
fpprbasnn |
|
2 |
|
fpprel |
|
3 |
|
nnz |
|
4 |
|
eluz4nn |
|
5 |
|
nnm1nn0 |
|
6 |
4 5
|
syl |
|
7 |
|
zexpcl |
|
8 |
3 6 7
|
syl2an |
|
9 |
8
|
zred |
|
10 |
4
|
nnrpd |
|
11 |
10
|
adantl |
|
12 |
9 11
|
modcld |
|
13 |
12
|
recnd |
|
14 |
|
1cnd |
|
15 |
|
nncn |
|
16 |
15
|
adantr |
|
17 |
|
nnne0 |
|
18 |
17
|
adantr |
|
19 |
13 14 16 18
|
mulcand |
|
20 |
|
oveq1 |
|
21 |
3
|
adantr |
|
22 |
|
modmulmodr |
|
23 |
21 9 11 22
|
syl3anc |
|
24 |
23
|
eqeq1d |
|
25 |
8
|
zcnd |
|
26 |
16 25
|
mulcomd |
|
27 |
|
expm1t |
|
28 |
27
|
eqcomd |
|
29 |
15 4 28
|
syl2an |
|
30 |
26 29
|
eqtrd |
|
31 |
30
|
oveq1d |
|
32 |
15
|
mulid1d |
|
33 |
32
|
adantr |
|
34 |
33
|
oveq1d |
|
35 |
31 34
|
eqeq12d |
|
36 |
35
|
biimpd |
|
37 |
24 36
|
sylbid |
|
38 |
20 37
|
syl5 |
|
39 |
19 38
|
sylbird |
|
40 |
39
|
a1d |
|
41 |
40
|
ex |
|
42 |
41
|
3impd |
|
43 |
2 42
|
sylbid |
|
44 |
1 43
|
mpcom |
|