Step |
Hyp |
Ref |
Expression |
1 |
|
zre |
|
2 |
|
chtval |
|
3 |
1 2
|
syl |
|
4 |
|
nnz |
|
5 |
|
ppisval |
|
6 |
1 5
|
syl |
|
7 |
|
flid |
|
8 |
7
|
oveq2d |
|
9 |
8
|
ineq1d |
|
10 |
6 9
|
eqtrd |
|
11 |
4 10
|
syl |
|
12 |
|
2nn |
|
13 |
|
nnuz |
|
14 |
12 13
|
eleqtri |
|
15 |
|
fzss1 |
|
16 |
14 15
|
ax-mp |
|
17 |
|
ssdif0 |
|
18 |
16 17
|
mpbi |
|
19 |
18
|
ineq1i |
|
20 |
|
0in |
|
21 |
19 20
|
eqtri |
|
22 |
21
|
a1i |
|
23 |
13
|
eleq2i |
|
24 |
|
fzpred |
|
25 |
23 24
|
sylbi |
|
26 |
25
|
eqcomd |
|
27 |
|
1p1e2 |
|
28 |
27
|
oveq1i |
|
29 |
28
|
a1i |
|
30 |
26 29
|
difeq12d |
|
31 |
|
difun2 |
|
32 |
|
fzpreddisj |
|
33 |
23 32
|
sylbi |
|
34 |
|
disjdif2 |
|
35 |
33 34
|
syl |
|
36 |
31 35
|
syl5eq |
|
37 |
30 36
|
eqtr3d |
|
38 |
37
|
ineq1d |
|
39 |
|
incom |
|
40 |
|
1nprm |
|
41 |
|
disjsn |
|
42 |
40 41
|
mpbir |
|
43 |
39 42
|
eqtr3i |
|
44 |
38 43
|
eqtrdi |
|
45 |
|
difininv |
|
46 |
22 44 45
|
syl2anc |
|
47 |
11 46
|
eqtrd |
|
48 |
47
|
adantl |
|
49 |
|
znnnlt1 |
|
50 |
49
|
biimpa |
|
51 |
|
incom |
|
52 |
|
isprm3 |
|
53 |
52
|
simplbi |
|
54 |
53
|
ssriv |
|
55 |
12
|
nnzi |
|
56 |
|
uzssico |
|
57 |
55 56
|
ax-mp |
|
58 |
54 57
|
sstri |
|
59 |
|
incom |
|
60 |
|
0xr |
|
61 |
60
|
a1i |
|
62 |
12
|
nnrei |
|
63 |
62
|
rexri |
|
64 |
63
|
a1i |
|
65 |
|
0le0 |
|
66 |
65
|
a1i |
|
67 |
1
|
adantr |
|
68 |
|
1red |
|
69 |
62
|
a1i |
|
70 |
|
simpr |
|
71 |
|
1lt2 |
|
72 |
71
|
a1i |
|
73 |
67 68 69 70 72
|
lttrd |
|
74 |
|
iccssico |
|
75 |
61 64 66 73 74
|
syl22anc |
|
76 |
|
pnfxr |
|
77 |
|
icodisj |
|
78 |
60 63 76 77
|
mp3an |
|
79 |
|
ssdisj |
|
80 |
75 78 79
|
sylancl |
|
81 |
59 80
|
syl5eqr |
|
82 |
|
ssdisj |
|
83 |
58 81 82
|
sylancr |
|
84 |
51 83
|
syl5eq |
|
85 |
|
1zzd |
|
86 |
|
simpl |
|
87 |
|
fzn |
|
88 |
87
|
biimpa |
|
89 |
85 86 70 88
|
syl21anc |
|
90 |
89
|
ineq1d |
|
91 |
90 20
|
eqtrdi |
|
92 |
84 91
|
eqtr4d |
|
93 |
50 92
|
syldan |
|
94 |
|
exmidd |
|
95 |
48 93 94
|
mpjaodan |
|
96 |
95
|
sumeq1d |
|
97 |
3 96
|
eqtrd |
|