Step |
Hyp |
Ref |
Expression |
1 |
|
eqid |
|
2 |
|
simpl |
|
3 |
|
prmnn |
|
4 |
3
|
nnzd |
|
5 |
|
1nn0 |
|
6 |
|
eluzmn |
|
7 |
4 5 6
|
sylancl |
|
8 |
|
fzss2 |
|
9 |
7 8
|
syl |
|
10 |
|
fz1ssfz0 |
|
11 |
9 10
|
sstrdi |
|
12 |
11
|
sselda |
|
13 |
|
bcval2 |
|
14 |
12 13
|
syl |
|
15 |
3
|
nnnn0d |
|
16 |
15
|
adantr |
|
17 |
|
elfzelz |
|
18 |
17
|
adantl |
|
19 |
|
bccl |
|
20 |
16 18 19
|
syl2anc |
|
21 |
20
|
nn0zd |
|
22 |
14 21
|
eqeltrrd |
|
23 |
|
elfznn |
|
24 |
23
|
adantl |
|
25 |
24
|
nnnn0d |
|
26 |
|
1zzd |
|
27 |
4
|
adantr |
|
28 |
|
simpr |
|
29 |
|
elfzm11 |
|
30 |
29
|
biimpa |
|
31 |
30
|
simp3d |
|
32 |
26 27 28 31
|
syl21anc |
|
33 |
|
ltsubnn0 |
|
34 |
33
|
imp |
|
35 |
16 25 32 34
|
syl21anc |
|
36 |
35
|
faccld |
|
37 |
36
|
nnzd |
|
38 |
25
|
faccld |
|
39 |
38
|
nnzd |
|
40 |
37 39
|
zmulcld |
|
41 |
37
|
zcnd |
|
42 |
39
|
zcnd |
|
43 |
|
facne0 |
|
44 |
35 43
|
syl |
|
45 |
|
facne0 |
|
46 |
25 45
|
syl |
|
47 |
41 42 44 46
|
mulne0d |
|
48 |
|
uzid |
|
49 |
4 48
|
syl |
|
50 |
|
dvdsfac |
|
51 |
3 49 50
|
syl2anc |
|
52 |
51
|
adantr |
|
53 |
16
|
nn0red |
|
54 |
24
|
nnrpd |
|
55 |
53 54
|
ltsubrpd |
|
56 |
|
prmndvdsfaclt |
|
57 |
56
|
imp |
|
58 |
2 35 55 57
|
syl21anc |
|
59 |
|
prmndvdsfaclt |
|
60 |
59
|
imp |
|
61 |
2 25 32 60
|
syl21anc |
|
62 |
|
ioran |
|
63 |
|
euclemma |
|
64 |
63
|
biimpd |
|
65 |
64
|
con3d |
|
66 |
62 65
|
syl5bir |
|
67 |
66
|
imp |
|
68 |
2 37 39 58 61 67
|
syl32anc |
|
69 |
1 2 22 40 47 52 68
|
dvdszzq |
|
70 |
69 14
|
breqtrrd |
|