Step |
Hyp |
Ref |
Expression |
1 |
|
elnn1uz2 |
|
2 |
|
5prm |
|
3 |
|
dvdsprime |
|
4 |
2 3
|
mpan |
|
5 |
|
1nn0 |
|
6 |
5
|
a1i |
|
7 |
|
simpl |
|
8 |
|
oveq1 |
|
9 |
8
|
oveq1d |
|
10 |
9
|
adantl |
|
11 |
7 10
|
eqeq12d |
|
12 |
|
df-5 |
|
13 |
|
4cn |
|
14 |
13
|
mulid2i |
|
15 |
14
|
eqcomi |
|
16 |
15
|
oveq1i |
|
17 |
12 16
|
eqtri |
|
18 |
17
|
a1i |
|
19 |
6 11 18
|
rspcedvd |
|
20 |
|
0nn0 |
|
21 |
20
|
a1i |
|
22 |
|
simpl |
|
23 |
|
oveq1 |
|
24 |
23
|
oveq1d |
|
25 |
24
|
adantl |
|
26 |
22 25
|
eqeq12d |
|
27 |
13
|
mul02i |
|
28 |
27
|
oveq1i |
|
29 |
|
0p1e1 |
|
30 |
28 29
|
eqtri |
|
31 |
30
|
eqcomi |
|
32 |
31
|
a1i |
|
33 |
21 26 32
|
rspcedvd |
|
34 |
19 33
|
jaoi |
|
35 |
4 34
|
syl6bi |
|
36 |
|
fveq2 |
|
37 |
|
fmtno1 |
|
38 |
36 37
|
eqtrdi |
|
39 |
38
|
breq2d |
|
40 |
|
oveq1 |
|
41 |
|
1p1e2 |
|
42 |
40 41
|
eqtrdi |
|
43 |
42
|
oveq2d |
|
44 |
|
sq2 |
|
45 |
43 44
|
eqtrdi |
|
46 |
45
|
oveq2d |
|
47 |
46
|
oveq1d |
|
48 |
47
|
eqeq2d |
|
49 |
48
|
rexbidv |
|
50 |
39 49
|
imbi12d |
|
51 |
35 50
|
syl5ibr |
|
52 |
|
fmtnofac2 |
|
53 |
|
id |
|
54 |
|
2nn0 |
|
55 |
54
|
a1i |
|
56 |
53 55
|
nn0mulcld |
|
57 |
56
|
adantl |
|
58 |
57
|
adantr |
|
59 |
|
simpr |
|
60 |
|
oveq1 |
|
61 |
60
|
oveq1d |
|
62 |
59 61
|
eqeqan12d |
|
63 |
|
eluzge2nn0 |
|
64 |
63
|
nn0cnd |
|
65 |
|
add1p1 |
|
66 |
64 65
|
syl |
|
67 |
66
|
eqcomd |
|
68 |
67
|
oveq2d |
|
69 |
|
2cnd |
|
70 |
|
peano2nn0 |
|
71 |
63 70
|
syl |
|
72 |
69 71
|
expp1d |
|
73 |
54
|
a1i |
|
74 |
73 71
|
nn0expcld |
|
75 |
74
|
nn0cnd |
|
76 |
75 69
|
mulcomd |
|
77 |
68 72 76
|
3eqtrd |
|
78 |
77
|
adantr |
|
79 |
78
|
oveq2d |
|
80 |
|
nn0cn |
|
81 |
80
|
adantl |
|
82 |
|
2cnd |
|
83 |
75
|
adantr |
|
84 |
81 82 83
|
mulassd |
|
85 |
79 84
|
eqtr4d |
|
86 |
85
|
3ad2antl1 |
|
87 |
86
|
adantr |
|
88 |
87
|
oveq1d |
|
89 |
58 62 88
|
rspcedvd |
|
90 |
89
|
rexlimdva2 |
|
91 |
52 90
|
mpd |
|
92 |
91
|
3exp |
|
93 |
51 92
|
jaoi |
|
94 |
1 93
|
sylbi |
|
95 |
94
|
3imp |
|