Step |
Hyp |
Ref |
Expression |
1 |
|
elznn0nn |
|
2 |
|
cnelprrecn |
|
3 |
2
|
a1i |
|
4 |
|
expcl |
|
5 |
4
|
ancoms |
|
6 |
|
c0ex |
|
7 |
|
ovex |
|
8 |
6 7
|
ifex |
|
9 |
8
|
a1i |
|
10 |
|
dvexp2 |
|
11 |
|
difssd |
|
12 |
|
eqid |
|
13 |
12
|
cnfldtopon |
|
14 |
13
|
toponrestid |
|
15 |
|
cnn0opn |
|
16 |
15
|
a1i |
|
17 |
3 5 9 10 11 14 12 16
|
dvmptres |
|
18 |
|
ifid |
|
19 |
|
id |
|
20 |
|
oveq1 |
|
21 |
20
|
oveq2d |
|
22 |
19 21
|
oveq12d |
|
23 |
|
eldifsn |
|
24 |
|
0z |
|
25 |
|
peano2zm |
|
26 |
24 25
|
ax-mp |
|
27 |
|
expclz |
|
28 |
26 27
|
mp3an3 |
|
29 |
23 28
|
sylbi |
|
30 |
29
|
adantl |
|
31 |
30
|
mul02d |
|
32 |
22 31
|
sylan9eqr |
|
33 |
32
|
ifeq1da |
|
34 |
18 33
|
eqtr3id |
|
35 |
34
|
mpteq2dva |
|
36 |
17 35
|
eqtr4d |
|
37 |
|
eldifi |
|
38 |
37
|
adantl |
|
39 |
|
simpll |
|
40 |
39
|
recnd |
|
41 |
|
nnnn0 |
|
42 |
41
|
ad2antlr |
|
43 |
|
expneg2 |
|
44 |
38 40 42 43
|
syl3anc |
|
45 |
44
|
mpteq2dva |
|
46 |
45
|
oveq2d |
|
47 |
2
|
a1i |
|
48 |
|
eldifsni |
|
49 |
48
|
adantl |
|
50 |
|
nnz |
|
51 |
50
|
ad2antlr |
|
52 |
38 49 51
|
expclzd |
|
53 |
38 49 51
|
expne0d |
|
54 |
|
eldifsn |
|
55 |
52 53 54
|
sylanbrc |
|
56 |
|
ovex |
|
57 |
56
|
a1i |
|
58 |
|
simpr |
|
59 |
|
eldifsn |
|
60 |
58 59
|
sylib |
|
61 |
|
reccl |
|
62 |
60 61
|
syl |
|
63 |
|
negex |
|
64 |
63
|
a1i |
|
65 |
|
simpr |
|
66 |
41
|
ad2antlr |
|
67 |
65 66
|
expcld |
|
68 |
56
|
a1i |
|
69 |
|
dvexp |
|
70 |
69
|
adantl |
|
71 |
|
difssd |
|
72 |
15
|
a1i |
|
73 |
47 67 68 70 71 14 12 72
|
dvmptres |
|
74 |
|
ax-1cn |
|
75 |
|
dvrec |
|
76 |
74 75
|
mp1i |
|
77 |
|
oveq2 |
|
78 |
|
oveq1 |
|
79 |
78
|
oveq2d |
|
80 |
79
|
negeqd |
|
81 |
47 47 55 57 62 64 73 76 77 80
|
dvmptco |
|
82 |
|
2z |
|
83 |
82
|
a1i |
|
84 |
|
expmulz |
|
85 |
38 49 51 83 84
|
syl22anc |
|
86 |
85
|
eqcomd |
|
87 |
86
|
oveq2d |
|
88 |
87
|
negeqd |
|
89 |
|
peano2zm |
|
90 |
51 89
|
syl |
|
91 |
38 49 90
|
expclzd |
|
92 |
40 91
|
mulneg1d |
|
93 |
88 92
|
oveq12d |
|
94 |
|
zmulcl |
|
95 |
51 82 94
|
sylancl |
|
96 |
38 49 95
|
expclzd |
|
97 |
38 49 95
|
expne0d |
|
98 |
96 97
|
reccld |
|
99 |
40 91
|
mulcld |
|
100 |
98 99
|
mul2negd |
|
101 |
98 40 91
|
mul12d |
|
102 |
38 49 95 90
|
expsubd |
|
103 |
|
nncn |
|
104 |
103
|
ad2antlr |
|
105 |
74
|
a1i |
|
106 |
95
|
zcnd |
|
107 |
104 105 106
|
sub32d |
|
108 |
104
|
times2d |
|
109 |
104 40
|
negsubd |
|
110 |
108 109
|
eqtrd |
|
111 |
110
|
oveq2d |
|
112 |
104 40
|
nncand |
|
113 |
111 112
|
eqtrd |
|
114 |
113
|
oveq1d |
|
115 |
107 114
|
eqtrd |
|
116 |
115
|
oveq2d |
|
117 |
91 96 97
|
divrec2d |
|
118 |
102 116 117
|
3eqtr3rd |
|
119 |
118
|
oveq2d |
|
120 |
101 119
|
eqtrd |
|
121 |
93 100 120
|
3eqtrd |
|
122 |
121
|
mpteq2dva |
|
123 |
46 81 122
|
3eqtrd |
|
124 |
36 123
|
jaoi |
|
125 |
1 124
|
sylbi |
|