Step |
Hyp |
Ref |
Expression |
1 |
|
prmdiv.1 |
|
2 |
|
nprmdvds1 |
|
3 |
2
|
3ad2ant1 |
|
4 |
|
prmz |
|
5 |
4
|
3ad2ant1 |
|
6 |
|
simp2 |
|
7 |
|
phiprm |
|
8 |
7
|
3ad2ant1 |
|
9 |
|
prmnn |
|
10 |
9
|
3ad2ant1 |
|
11 |
|
nnm1nn0 |
|
12 |
10 11
|
syl |
|
13 |
8 12
|
eqeltrd |
|
14 |
|
zexpcl |
|
15 |
6 13 14
|
syl2anc |
|
16 |
|
1z |
|
17 |
|
zsubcl |
|
18 |
15 16 17
|
sylancl |
|
19 |
|
prmuz2 |
|
20 |
19
|
3ad2ant1 |
|
21 |
|
uznn0sub |
|
22 |
20 21
|
syl |
|
23 |
|
zexpcl |
|
24 |
6 22 23
|
syl2anc |
|
25 |
24
|
zred |
|
26 |
25 10
|
nndivred |
|
27 |
26
|
flcld |
|
28 |
6 27
|
zmulcld |
|
29 |
5 28
|
zmulcld |
|
30 |
6 5
|
gcdcomd |
|
31 |
|
coprm |
|
32 |
31
|
biimp3a |
|
33 |
30 32
|
eqtrd |
|
34 |
|
eulerth |
|
35 |
10 6 33 34
|
syl3anc |
|
36 |
|
1zzd |
|
37 |
|
moddvds |
|
38 |
10 15 36 37
|
syl3anc |
|
39 |
35 38
|
mpbid |
|
40 |
|
dvdsmul1 |
|
41 |
5 28 40
|
syl2anc |
|
42 |
5 18 29 39 41
|
dvds2subd |
|
43 |
6
|
zcnd |
|
44 |
24
|
zcnd |
|
45 |
5 27
|
zmulcld |
|
46 |
45
|
zcnd |
|
47 |
43 44 46
|
subdid |
|
48 |
10
|
nnrpd |
|
49 |
|
modval |
|
50 |
25 48 49
|
syl2anc |
|
51 |
1 50
|
syl5eq |
|
52 |
51
|
oveq2d |
|
53 |
|
2m1e1 |
|
54 |
53
|
oveq2i |
|
55 |
8 54
|
eqtr4di |
|
56 |
10
|
nncnd |
|
57 |
|
2cnd |
|
58 |
|
1cnd |
|
59 |
56 57 58
|
subsubd |
|
60 |
55 59
|
eqtrd |
|
61 |
60
|
oveq2d |
|
62 |
43 22
|
expp1d |
|
63 |
44 43
|
mulcomd |
|
64 |
61 62 63
|
3eqtrd |
|
65 |
27
|
zcnd |
|
66 |
56 43 65
|
mul12d |
|
67 |
64 66
|
oveq12d |
|
68 |
47 52 67
|
3eqtr4d |
|
69 |
68
|
oveq1d |
|
70 |
15
|
zcnd |
|
71 |
29
|
zcnd |
|
72 |
70 71 58
|
sub32d |
|
73 |
69 72
|
eqtrd |
|
74 |
42 73
|
breqtrrd |
|
75 |
|
oveq2 |
|
76 |
75
|
oveq1d |
|
77 |
76
|
breq2d |
|
78 |
74 77
|
syl5ibcom |
|
79 |
43
|
mul01d |
|
80 |
79
|
oveq1d |
|
81 |
|
df-neg |
|
82 |
80 81
|
eqtr4di |
|
83 |
82
|
breq2d |
|
84 |
|
dvdsnegb |
|
85 |
5 16 84
|
sylancl |
|
86 |
83 85
|
bitr4d |
|
87 |
78 86
|
sylibd |
|
88 |
3 87
|
mtod |
|
89 |
|
zmodfz |
|
90 |
24 10 89
|
syl2anc |
|
91 |
1 90
|
eqeltrid |
|
92 |
|
nn0uz |
|
93 |
12 92
|
eleqtrdi |
|
94 |
|
elfzp12 |
|
95 |
93 94
|
syl |
|
96 |
91 95
|
mpbid |
|
97 |
96
|
ord |
|
98 |
88 97
|
mpd |
|
99 |
|
1e0p1 |
|
100 |
99
|
oveq1i |
|
101 |
98 100
|
eleqtrrdi |
|
102 |
101 74
|
jca |
|