Step |
Hyp |
Ref |
Expression |
1 |
|
elfzelz |
|
2 |
1
|
adantl |
|
3 |
|
peano2zm |
|
4 |
2 3
|
syl |
|
5 |
4
|
zcnd |
|
6 |
2
|
peano2zd |
|
7 |
6
|
zcnd |
|
8 |
5 7
|
mulcomd |
|
9 |
2
|
zcnd |
|
10 |
|
ax-1cn |
|
11 |
|
subsq |
|
12 |
9 10 11
|
sylancl |
|
13 |
9
|
sqvald |
|
14 |
|
sq1 |
|
15 |
14
|
a1i |
|
16 |
13 15
|
oveq12d |
|
17 |
8 12 16
|
3eqtr2d |
|
18 |
17
|
breq2d |
|
19 |
|
fz1ssfz0 |
|
20 |
|
simpr |
|
21 |
19 20
|
sselid |
|
22 |
21
|
biantrurd |
|
23 |
18 22
|
bitrd |
|
24 |
|
simpl |
|
25 |
|
euclemma |
|
26 |
24 4 6 25
|
syl3anc |
|
27 |
|
prmnn |
|
28 |
|
fzm1ndvds |
|
29 |
27 28
|
sylan |
|
30 |
|
eqid |
|
31 |
30
|
prmdiveq |
|
32 |
24 2 29 31
|
syl3anc |
|
33 |
23 26 32
|
3bitr3rd |
|
34 |
24 27
|
syl |
|
35 |
|
1zzd |
|
36 |
|
moddvds |
|
37 |
34 2 35 36
|
syl3anc |
|
38 |
|
elfznn |
|
39 |
38
|
adantl |
|
40 |
39
|
nnred |
|
41 |
34
|
nnrpd |
|
42 |
39
|
nnnn0d |
|
43 |
42
|
nn0ge0d |
|
44 |
|
elfzle2 |
|
45 |
44
|
adantl |
|
46 |
|
prmz |
|
47 |
|
zltlem1 |
|
48 |
1 46 47
|
syl2anr |
|
49 |
45 48
|
mpbird |
|
50 |
|
modid |
|
51 |
40 41 43 49 50
|
syl22anc |
|
52 |
34
|
nnred |
|
53 |
|
prmuz2 |
|
54 |
24 53
|
syl |
|
55 |
|
eluz2gt1 |
|
56 |
54 55
|
syl |
|
57 |
|
1mod |
|
58 |
52 56 57
|
syl2anc |
|
59 |
51 58
|
eqeq12d |
|
60 |
37 59
|
bitr3d |
|
61 |
35
|
znegcld |
|
62 |
|
moddvds |
|
63 |
34 2 61 62
|
syl3anc |
|
64 |
34
|
nncnd |
|
65 |
64
|
mulid2d |
|
66 |
65
|
oveq2d |
|
67 |
|
neg1cn |
|
68 |
|
addcom |
|
69 |
67 64 68
|
sylancr |
|
70 |
|
negsub |
|
71 |
64 10 70
|
sylancl |
|
72 |
66 69 71
|
3eqtrd |
|
73 |
72
|
oveq1d |
|
74 |
|
neg1rr |
|
75 |
74
|
a1i |
|
76 |
|
modcyc |
|
77 |
75 41 35 76
|
syl3anc |
|
78 |
|
peano2rem |
|
79 |
52 78
|
syl |
|
80 |
|
nnm1nn0 |
|
81 |
34 80
|
syl |
|
82 |
81
|
nn0ge0d |
|
83 |
52
|
ltm1d |
|
84 |
|
modid |
|
85 |
79 41 82 83 84
|
syl22anc |
|
86 |
73 77 85
|
3eqtr3d |
|
87 |
51 86
|
eqeq12d |
|
88 |
|
subneg |
|
89 |
9 10 88
|
sylancl |
|
90 |
89
|
breq2d |
|
91 |
63 87 90
|
3bitr3rd |
|
92 |
60 91
|
orbi12d |
|
93 |
33 92
|
bitrd |
|