Step |
Hyp |
Ref |
Expression |
1 |
|
2nn |
|
2 |
|
fpprel |
|
3 |
1 2
|
ax-mp |
|
4 |
|
eluz4nn |
|
5 |
4
|
adantr |
|
6 |
|
eluzelz |
|
7 |
|
zeo2ALTV |
|
8 |
6 7
|
syl |
|
9 |
8
|
adantr |
|
10 |
9
|
biimprd |
|
11 |
|
nnennexALTV |
|
12 |
5 10 11
|
syl6an |
|
13 |
|
oveq1 |
|
14 |
13
|
oveq2d |
|
15 |
|
id |
|
16 |
14 15
|
oveq12d |
|
17 |
16
|
eqeq1d |
|
18 |
17
|
adantl |
|
19 |
|
2z |
|
20 |
1
|
a1i |
|
21 |
|
id |
|
22 |
20 21
|
nnmulcld |
|
23 |
|
nnm1nn0 |
|
24 |
22 23
|
syl |
|
25 |
|
zexpcl |
|
26 |
19 24 25
|
sylancr |
|
27 |
22
|
nnrpd |
|
28 |
|
modmuladdim |
|
29 |
26 27 28
|
syl2anc |
|
30 |
24
|
adantr |
|
31 |
19 30 25
|
sylancr |
|
32 |
31
|
zcnd |
|
33 |
|
zcn |
|
34 |
33
|
adantl |
|
35 |
|
2cnd |
|
36 |
|
nncn |
|
37 |
36
|
adantr |
|
38 |
35 37
|
mulcld |
|
39 |
34 38
|
mulcld |
|
40 |
|
1cnd |
|
41 |
|
subadd |
|
42 |
|
eqcom |
|
43 |
41 42
|
bitrdi |
|
44 |
32 39 40 43
|
syl3anc |
|
45 |
|
2cnd |
|
46 |
45 36
|
mulcld |
|
47 |
|
1cnd |
|
48 |
46 47
|
subcld |
|
49 |
48
|
adantr |
|
50 |
|
npcan1 |
|
51 |
49 50
|
syl |
|
52 |
51
|
eqcomd |
|
53 |
52
|
oveq2d |
|
54 |
|
2t1e2 |
|
55 |
54
|
eqcomi |
|
56 |
55
|
oveq2i |
|
57 |
|
sub1m1 |
|
58 |
38 57
|
syl |
|
59 |
35 37 40
|
subdid |
|
60 |
56 58 59
|
3eqtr4a |
|
61 |
|
2nn0 |
|
62 |
61
|
a1i |
|
63 |
|
nnm1nn0 |
|
64 |
63
|
adantr |
|
65 |
62 64
|
nn0mulcld |
|
66 |
60 65
|
eqeltrd |
|
67 |
35 66
|
expp1d |
|
68 |
35 66
|
expcld |
|
69 |
68 35
|
mulcomd |
|
70 |
67 69
|
eqtrd |
|
71 |
53 70
|
eqtrd |
|
72 |
34 35 37
|
mul12d |
|
73 |
71 72
|
oveq12d |
|
74 |
34 37
|
mulcld |
|
75 |
35 68 74
|
subdid |
|
76 |
75
|
eqcomd |
|
77 |
73 76
|
eqtrd |
|
78 |
77
|
eqeq1d |
|
79 |
|
zexpcl |
|
80 |
19 66 79
|
sylancr |
|
81 |
|
simpr |
|
82 |
|
nnz |
|
83 |
82
|
adantr |
|
84 |
81 83
|
zmulcld |
|
85 |
80 84
|
zsubcld |
|
86 |
|
m2even |
|
87 |
85 86
|
syl |
|
88 |
|
1oddALTV |
|
89 |
|
zneoALTV |
|
90 |
87 88 89
|
sylancl |
|
91 |
|
eqneqall |
|
92 |
90 91
|
syl5com |
|
93 |
78 92
|
sylbid |
|
94 |
44 93
|
sylbird |
|
95 |
94
|
rexlimdva |
|
96 |
29 95
|
syld |
|
97 |
96
|
adantl |
|
98 |
97
|
adantr |
|
99 |
18 98
|
sylbid |
|
100 |
99
|
ex |
|
101 |
100
|
rexlimdva |
|
102 |
101
|
com23 |
|
103 |
102
|
imp |
|
104 |
12 103
|
syld |
|
105 |
104
|
3adant2 |
|
106 |
3 105
|
sylbi |
|
107 |
106
|
pm2.18d |
|