Step |
Hyp |
Ref |
Expression |
1 |
|
proot1ex.g |
|
2 |
|
proot1ex.o |
|
3 |
|
neg1cn |
|
4 |
|
2rp |
|
5 |
|
nnrp |
|
6 |
|
rpdivcl |
|
7 |
4 5 6
|
sylancr |
|
8 |
7
|
rpcnd |
|
9 |
|
cxpcl |
|
10 |
3 8 9
|
sylancr |
|
11 |
3
|
a1i |
|
12 |
|
neg1ne0 |
|
13 |
12
|
a1i |
|
14 |
11 13 8
|
cxpne0d |
|
15 |
|
eldifsn |
|
16 |
10 14 15
|
sylanbrc |
|
17 |
3
|
a1i |
|
18 |
12
|
a1i |
|
19 |
|
nn0cn |
|
20 |
|
mulcl |
|
21 |
8 19 20
|
syl2an |
|
22 |
17 18 21
|
cxpefd |
|
23 |
22
|
eqeq1d |
|
24 |
|
logcl |
|
25 |
3 12 24
|
mp2an |
|
26 |
|
mulcl |
|
27 |
21 25 26
|
sylancl |
|
28 |
|
efeq1 |
|
29 |
27 28
|
syl |
|
30 |
|
2cn |
|
31 |
30
|
a1i |
|
32 |
|
nncn |
|
33 |
32
|
adantr |
|
34 |
19
|
adantl |
|
35 |
|
nnne0 |
|
36 |
35
|
adantr |
|
37 |
31 33 34 36
|
div13d |
|
38 |
|
logm1 |
|
39 |
38
|
a1i |
|
40 |
37 39
|
oveq12d |
|
41 |
34 33 36
|
divcld |
|
42 |
|
ax-icn |
|
43 |
|
picn |
|
44 |
42 43
|
mulcli |
|
45 |
44
|
a1i |
|
46 |
41 31 45
|
mulassd |
|
47 |
42
|
a1i |
|
48 |
43
|
a1i |
|
49 |
31 47 48
|
mul12d |
|
50 |
49
|
oveq2d |
|
51 |
40 46 50
|
3eqtrd |
|
52 |
51
|
oveq1d |
|
53 |
30 43
|
mulcli |
|
54 |
42 53
|
mulcli |
|
55 |
54
|
a1i |
|
56 |
|
ine0 |
|
57 |
|
2ne0 |
|
58 |
|
pire |
|
59 |
|
pipos |
|
60 |
58 59
|
gt0ne0ii |
|
61 |
30 43 57 60
|
mulne0i |
|
62 |
42 53 56 61
|
mulne0i |
|
63 |
62
|
a1i |
|
64 |
41 55 63
|
divcan4d |
|
65 |
52 64
|
eqtrd |
|
66 |
65
|
eleq1d |
|
67 |
23 29 66
|
3bitrd |
|
68 |
8
|
adantr |
|
69 |
|
simpr |
|
70 |
17 68 69
|
cxpmul2d |
|
71 |
|
cnfldexp |
|
72 |
10 71
|
sylan |
|
73 |
|
cnring |
|
74 |
|
cnfldbas |
|
75 |
|
cnfld0 |
|
76 |
|
cndrng |
|
77 |
74 75 76
|
drngui |
|
78 |
|
eqid |
|
79 |
77 78
|
unitsubm |
|
80 |
73 79
|
mp1i |
|
81 |
16
|
adantr |
|
82 |
|
eqid |
|
83 |
|
eqid |
|
84 |
82 1 83
|
submmulg |
|
85 |
80 69 81 84
|
syl3anc |
|
86 |
70 72 85
|
3eqtr2rd |
|
87 |
86
|
eqeq1d |
|
88 |
|
nnz |
|
89 |
88
|
adantr |
|
90 |
|
nn0z |
|
91 |
90
|
adantl |
|
92 |
|
dvdsval2 |
|
93 |
89 36 91 92
|
syl3anc |
|
94 |
67 87 93
|
3bitr4rd |
|
95 |
94
|
ralrimiva |
|
96 |
77 1
|
unitgrp |
|
97 |
73 96
|
mp1i |
|
98 |
|
nnnn0 |
|
99 |
77 1
|
unitgrpbas |
|
100 |
|
cnfld1 |
|
101 |
77 1 100
|
unitgrpid |
|
102 |
73 101
|
ax-mp |
|
103 |
99 2 83 102
|
odeq |
|
104 |
97 16 98 103
|
syl3anc |
|
105 |
95 104
|
mpbird |
|
106 |
105
|
eqcomd |
|
107 |
99 2
|
odf |
|
108 |
|
ffn |
|
109 |
107 108
|
ax-mp |
|
110 |
|
fniniseg |
|
111 |
109 110
|
mp1i |
|
112 |
16 106 111
|
mpbir2and |
|