Step |
Hyp |
Ref |
Expression |
1 |
|
1arith.1 |
|
2 |
|
1arith.2 |
|
3 |
|
prmex |
|
4 |
3
|
mptex |
|
5 |
4 1
|
fnmpti |
|
6 |
1
|
1arithlem3 |
|
7 |
|
nn0ex |
|
8 |
7 3
|
elmap |
|
9 |
6 8
|
sylibr |
|
10 |
|
fzfi |
|
11 |
|
ffn |
|
12 |
|
elpreima |
|
13 |
6 11 12
|
3syl |
|
14 |
1
|
1arithlem2 |
|
15 |
14
|
eleq1d |
|
16 |
|
prmz |
|
17 |
|
id |
|
18 |
|
dvdsle |
|
19 |
16 17 18
|
syl2anr |
|
20 |
|
pcelnn |
|
21 |
20
|
ancoms |
|
22 |
|
prmnn |
|
23 |
|
nnuz |
|
24 |
22 23
|
eleqtrdi |
|
25 |
|
nnz |
|
26 |
|
elfz5 |
|
27 |
24 25 26
|
syl2anr |
|
28 |
19 21 27
|
3imtr4d |
|
29 |
15 28
|
sylbid |
|
30 |
29
|
expimpd |
|
31 |
13 30
|
sylbid |
|
32 |
31
|
ssrdv |
|
33 |
|
ssfi |
|
34 |
10 32 33
|
sylancr |
|
35 |
|
cnveq |
|
36 |
35
|
imaeq1d |
|
37 |
36
|
eleq1d |
|
38 |
37 2
|
elrab2 |
|
39 |
9 34 38
|
sylanbrc |
|
40 |
39
|
rgen |
|
41 |
|
ffnfv |
|
42 |
5 40 41
|
mpbir2an |
|
43 |
14
|
adantlr |
|
44 |
1
|
1arithlem2 |
|
45 |
44
|
adantll |
|
46 |
43 45
|
eqeq12d |
|
47 |
46
|
ralbidva |
|
48 |
1
|
1arithlem3 |
|
49 |
|
ffn |
|
50 |
|
eqfnfv |
|
51 |
11 49 50
|
syl2an |
|
52 |
6 48 51
|
syl2an |
|
53 |
|
nnnn0 |
|
54 |
|
nnnn0 |
|
55 |
|
pc11 |
|
56 |
53 54 55
|
syl2an |
|
57 |
47 52 56
|
3bitr4d |
|
58 |
57
|
biimpd |
|
59 |
58
|
rgen2 |
|
60 |
|
dff13 |
|
61 |
42 59 60
|
mpbir2an |
|
62 |
|
eqid |
|
63 |
|
cnveq |
|
64 |
63
|
imaeq1d |
|
65 |
64
|
eleq1d |
|
66 |
65 2
|
elrab2 |
|
67 |
66
|
simplbi |
|
68 |
7 3
|
elmap |
|
69 |
67 68
|
sylib |
|
70 |
69
|
ad2antrr |
|
71 |
|
simplr |
|
72 |
|
0re |
|
73 |
|
ifcl |
|
74 |
71 72 73
|
sylancl |
|
75 |
|
max1 |
|
76 |
72 71 75
|
sylancr |
|
77 |
|
flge0nn0 |
|
78 |
74 76 77
|
syl2anc |
|
79 |
|
nn0p1nn |
|
80 |
78 79
|
syl |
|
81 |
71
|
adantr |
|
82 |
80
|
adantr |
|
83 |
82
|
nnred |
|
84 |
16
|
ssriv |
|
85 |
|
zssre |
|
86 |
84 85
|
sstri |
|
87 |
|
simprl |
|
88 |
86 87
|
sseldi |
|
89 |
74
|
adantr |
|
90 |
|
max2 |
|
91 |
72 81 90
|
sylancr |
|
92 |
|
flltp1 |
|
93 |
89 92
|
syl |
|
94 |
81 89 83 91 93
|
lelttrd |
|
95 |
|
simprr |
|
96 |
81 83 88 94 95
|
ltletrd |
|
97 |
81 88
|
ltnled |
|
98 |
96 97
|
mpbid |
|
99 |
87
|
biantrurd |
|
100 |
70
|
adantr |
|
101 |
|
ffn |
|
102 |
|
elpreima |
|
103 |
100 101 102
|
3syl |
|
104 |
99 103
|
bitr4d |
|
105 |
|
simplr |
|
106 |
|
breq1 |
|
107 |
106
|
rspccv |
|
108 |
105 107
|
syl |
|
109 |
104 108
|
sylbid |
|
110 |
98 109
|
mtod |
|
111 |
100 87
|
ffvelrnd |
|
112 |
|
elnn0 |
|
113 |
111 112
|
sylib |
|
114 |
113
|
ord |
|
115 |
110 114
|
mpd |
|
116 |
1 62 70 80 115
|
1arithlem4 |
|
117 |
|
cnvimass |
|
118 |
69
|
fdmd |
|
119 |
118 86
|
eqsstrdi |
|
120 |
117 119
|
sstrid |
|
121 |
66
|
simprbi |
|
122 |
|
fimaxre2 |
|
123 |
120 121 122
|
syl2anc |
|
124 |
116 123
|
r19.29a |
|
125 |
124
|
rgen |
|
126 |
|
dffo3 |
|
127 |
42 125 126
|
mpbir2an |
|
128 |
|
df-f1o |
|
129 |
61 127 128
|
mpbir2an |
|