Step |
Hyp |
Ref |
Expression |
1 |
|
zcn |
|
2 |
1
|
3ad2ant2 |
|
3 |
|
1cnd |
|
4 |
|
zcn |
|
5 |
4
|
3ad2ant3 |
|
6 |
2 3 5
|
add32d |
|
7 |
6
|
fvoveq1d |
|
8 |
7
|
3ad2ant1 |
|
9 |
8
|
preq2d |
|
10 |
|
zaddcl |
|
11 |
10
|
3adant1 |
|
12 |
|
eluz2nn |
|
13 |
12
|
3ad2ant1 |
|
14 |
11 13
|
zmodcld |
|
15 |
14
|
adantr |
|
16 |
|
uz2m1nn |
|
17 |
16
|
3ad2ant1 |
|
18 |
17
|
adantr |
|
19 |
|
simpr |
|
20 |
|
elfzo0 |
|
21 |
15 18 19 20
|
syl3anbrc |
|
22 |
|
fveq2 |
|
23 |
|
fvoveq1 |
|
24 |
22 23
|
preq12d |
|
25 |
24
|
eleq1d |
|
26 |
25
|
rspcv |
|
27 |
21 26
|
syl |
|
28 |
10
|
zred |
|
29 |
28
|
3adant1 |
|
30 |
29
|
adantr |
|
31 |
12
|
nnrpd |
|
32 |
31
|
3ad2ant1 |
|
33 |
32
|
adantr |
|
34 |
|
modltm1p1mod |
|
35 |
30 33 19 34
|
syl3anc |
|
36 |
35
|
fveq2d |
|
37 |
36
|
preq2d |
|
38 |
37
|
eleq1d |
|
39 |
27 38
|
sylibrd |
|
40 |
39
|
impancom |
|
41 |
40
|
3adant3 |
|
42 |
|
zmodfzo |
|
43 |
11 13 42
|
syl2anc |
|
44 |
|
elfzonlteqm1 |
|
45 |
44
|
eqcomd |
|
46 |
45
|
ex |
|
47 |
43 46
|
syl |
|
48 |
|
fveq2 |
|
49 |
48
|
adantl |
|
50 |
|
zre |
|
51 |
|
zre |
|
52 |
|
readdcl |
|
53 |
50 51 52
|
syl2an |
|
54 |
53
|
3adant1 |
|
55 |
54 32
|
jca |
|
56 |
55
|
adantr |
|
57 |
|
simpr |
|
58 |
57
|
eqcomd |
|
59 |
|
modm1p1mod0 |
|
60 |
56 58 59
|
sylc |
|
61 |
60
|
eqcomd |
|
62 |
61
|
fveq2d |
|
63 |
49 62
|
preq12d |
|
64 |
63
|
eleq1d |
|
65 |
64
|
biimpd |
|
66 |
65
|
ex |
|
67 |
47 66
|
syld |
|
68 |
67
|
com23 |
|
69 |
68
|
imp |
|
70 |
69
|
3adant2 |
|
71 |
41 70
|
pm2.61d |
|
72 |
9 71
|
eqeltrd |
|