Step |
Hyp |
Ref |
Expression |
1 |
|
prmnn |
|
2 |
1
|
adantr |
|
3 |
2
|
nnred |
|
4 |
|
0red |
|
5 |
2
|
nngt0d |
|
6 |
4 3 5
|
ltled |
|
7 |
|
eluzelre |
|
8 |
7
|
adantl |
|
9 |
|
eluz2n0 |
|
10 |
9
|
adantl |
|
11 |
8 10
|
rereccld |
|
12 |
3 6 11
|
recxpcld |
|
13 |
|
eluz2gt1 |
|
14 |
|
recgt1i |
|
15 |
7 13 14
|
syl2anc |
|
16 |
15
|
simprd |
|
17 |
16
|
adantl |
|
18 |
1
|
nnred |
|
19 |
18
|
adantr |
|
20 |
|
prmgt1 |
|
21 |
20
|
adantr |
|
22 |
|
1red |
|
23 |
19 21 11 22
|
cxpltd |
|
24 |
17 23
|
mpbid |
|
25 |
2
|
nncnd |
|
26 |
25
|
cxp1d |
|
27 |
24 26
|
breqtrd |
|
28 |
12 27
|
ltned |
|
29 |
28
|
neneqd |
|
30 |
29
|
adantr |
|
31 |
25
|
cxp0d |
|
32 |
15
|
simpld |
|
33 |
32
|
adantl |
|
34 |
19 21 4 11
|
cxpltd |
|
35 |
33 34
|
mpbid |
|
36 |
31 35
|
eqbrtrrd |
|
37 |
22 36
|
gtned |
|
38 |
37
|
neneqd |
|
39 |
38
|
adantr |
|
40 |
|
dvdsprime |
|
41 |
40
|
adantlr |
|
42 |
41
|
biimpd |
|
43 |
30 39 42
|
mtord |
|
44 |
|
nan |
|
45 |
43 44
|
mpbir |
|
46 |
|
prmz |
|
47 |
|
eluz2nn |
|
48 |
|
zrtdvds |
|
49 |
46 47 48
|
syl3an12 |
|
50 |
49
|
3expia |
|
51 |
50
|
ancld |
|
52 |
45 51
|
mtod |
|
53 |
1
|
nnrpd |
|
54 |
53
|
3ad2ant1 |
|
55 |
7
|
3ad2ant2 |
|
56 |
9
|
3ad2ant2 |
|
57 |
55 56
|
rereccld |
|
58 |
54 57
|
cxpgt0d |
|
59 |
58
|
3expia |
|
60 |
59
|
ancld |
|
61 |
|
elnnz |
|
62 |
60 61
|
imbitrrdi |
|
63 |
52 62
|
mtod |
|
64 |
|
zrtelqelz |
|
65 |
46 47 64
|
syl3an12 |
|
66 |
65
|
3expia |
|
67 |
63 66
|
mtod |
|
68 |
12 67
|
eldifd |
|