Step |
Hyp |
Ref |
Expression |
1 |
|
znf1o.y |
|
2 |
|
znf1o.b |
|
3 |
|
znf1o.f |
|
4 |
|
znf1o.w |
|
5 |
1
|
zncrng |
|
6 |
|
crngring |
|
7 |
|
eqid |
|
8 |
7
|
zrhrhm |
|
9 |
|
zringbas |
|
10 |
9 2
|
rhmf |
|
11 |
5 6 8 10
|
4syl |
|
12 |
|
sseq1 |
|
13 |
|
sseq1 |
|
14 |
|
ssid |
|
15 |
|
elfzoelz |
|
16 |
15
|
ssriv |
|
17 |
12 13 14 16
|
keephyp |
|
18 |
4 17
|
eqsstri |
|
19 |
|
fssres |
|
20 |
11 18 19
|
sylancl |
|
21 |
3
|
feq1i |
|
22 |
20 21
|
sylibr |
|
23 |
3
|
fveq1i |
|
24 |
|
fvres |
|
25 |
24
|
ad2antrl |
|
26 |
23 25
|
syl5eq |
|
27 |
3
|
fveq1i |
|
28 |
|
fvres |
|
29 |
28
|
ad2antll |
|
30 |
27 29
|
syl5eq |
|
31 |
26 30
|
eqeq12d |
|
32 |
|
simpl |
|
33 |
|
simprl |
|
34 |
18 33
|
sseldi |
|
35 |
|
simprr |
|
36 |
18 35
|
sseldi |
|
37 |
1 7
|
zndvds |
|
38 |
32 34 36 37
|
syl3anc |
|
39 |
|
elnn0 |
|
40 |
|
simpl |
|
41 |
|
simprl |
|
42 |
18 41
|
sseldi |
|
43 |
|
simprr |
|
44 |
18 43
|
sseldi |
|
45 |
|
moddvds |
|
46 |
40 42 44 45
|
syl3anc |
|
47 |
42
|
zred |
|
48 |
|
nnrp |
|
49 |
48
|
adantr |
|
50 |
|
nnne0 |
|
51 |
|
ifnefalse |
|
52 |
50 51
|
syl |
|
53 |
4 52
|
syl5eq |
|
54 |
53
|
adantr |
|
55 |
41 54
|
eleqtrd |
|
56 |
|
elfzole1 |
|
57 |
55 56
|
syl |
|
58 |
|
elfzolt2 |
|
59 |
55 58
|
syl |
|
60 |
|
modid |
|
61 |
47 49 57 59 60
|
syl22anc |
|
62 |
44
|
zred |
|
63 |
43 54
|
eleqtrd |
|
64 |
|
elfzole1 |
|
65 |
63 64
|
syl |
|
66 |
|
elfzolt2 |
|
67 |
63 66
|
syl |
|
68 |
|
modid |
|
69 |
62 49 65 67 68
|
syl22anc |
|
70 |
61 69
|
eqeq12d |
|
71 |
46 70
|
bitr3d |
|
72 |
|
simpl |
|
73 |
72
|
breq1d |
|
74 |
|
id |
|
75 |
|
0nn0 |
|
76 |
74 75
|
eqeltrdi |
|
77 |
76 34
|
sylan |
|
78 |
76 36
|
sylan |
|
79 |
77 78
|
zsubcld |
|
80 |
|
0dvds |
|
81 |
79 80
|
syl |
|
82 |
77
|
zcnd |
|
83 |
78
|
zcnd |
|
84 |
82 83
|
subeq0ad |
|
85 |
73 81 84
|
3bitrd |
|
86 |
71 85
|
jaoian |
|
87 |
39 86
|
sylanb |
|
88 |
31 38 87
|
3bitrd |
|
89 |
88
|
biimpd |
|
90 |
89
|
ralrimivva |
|
91 |
|
dff13 |
|
92 |
22 90 91
|
sylanbrc |
|
93 |
|
zmodfzo |
|
94 |
93
|
ancoms |
|
95 |
53
|
adantr |
|
96 |
94 95
|
eleqtrrd |
|
97 |
|
zre |
|
98 |
|
modabs2 |
|
99 |
97 48 98
|
syl2anr |
|
100 |
|
simpl |
|
101 |
16 94
|
sseldi |
|
102 |
|
simpr |
|
103 |
|
moddvds |
|
104 |
100 101 102 103
|
syl3anc |
|
105 |
99 104
|
mpbid |
|
106 |
|
nnnn0 |
|
107 |
106
|
adantr |
|
108 |
1 7
|
zndvds |
|
109 |
107 101 102 108
|
syl3anc |
|
110 |
105 109
|
mpbird |
|
111 |
110
|
eqcomd |
|
112 |
|
fveq2 |
|
113 |
112
|
rspceeqv |
|
114 |
96 111 113
|
syl2anc |
|
115 |
|
iftrue |
|
116 |
115
|
eleq2d |
|
117 |
116
|
biimpar |
|
118 |
117 4
|
eleqtrrdi |
|
119 |
|
eqidd |
|
120 |
|
fveq2 |
|
121 |
120
|
rspceeqv |
|
122 |
118 119 121
|
syl2anc |
|
123 |
114 122
|
jaoian |
|
124 |
39 123
|
sylanb |
|
125 |
27 28
|
syl5eq |
|
126 |
125
|
eqeq2d |
|
127 |
126
|
rexbiia |
|
128 |
124 127
|
sylibr |
|
129 |
128
|
ralrimiva |
|
130 |
1 2 7
|
znzrhfo |
|
131 |
|
fofn |
|
132 |
|
eqeq1 |
|
133 |
132
|
rexbidv |
|
134 |
133
|
ralrn |
|
135 |
130 131 134
|
3syl |
|
136 |
129 135
|
mpbird |
|
137 |
|
forn |
|
138 |
130 137
|
syl |
|
139 |
138
|
raleqdv |
|
140 |
136 139
|
mpbid |
|
141 |
|
dffo3 |
|
142 |
22 140 141
|
sylanbrc |
|
143 |
|
df-f1o |
|
144 |
92 142 143
|
sylanbrc |
|