Step |
Hyp |
Ref |
Expression |
1 |
|
eluzelre |
|
2 |
|
8re |
|
3 |
2
|
a1i |
|
4 |
1 3
|
leloed |
|
5 |
|
eluzelz |
|
6 |
|
7nn |
|
7 |
6
|
nnzi |
|
8 |
|
zleltp1 |
|
9 |
5 7 8
|
sylancl |
|
10 |
|
7re |
|
11 |
10
|
a1i |
|
12 |
1 11
|
leloed |
|
13 |
|
7p1e8 |
|
14 |
13
|
breq2i |
|
15 |
14
|
a1i |
|
16 |
9 12 15
|
3bitr3rd |
|
17 |
|
6nn |
|
18 |
17
|
nnzi |
|
19 |
|
zleltp1 |
|
20 |
5 18 19
|
sylancl |
|
21 |
|
6re |
|
22 |
21
|
a1i |
|
23 |
1 22
|
leloed |
|
24 |
|
6p1e7 |
|
25 |
24
|
breq2i |
|
26 |
25
|
a1i |
|
27 |
20 23 26
|
3bitr3rd |
|
28 |
|
5nn |
|
29 |
28
|
nnzi |
|
30 |
|
zleltp1 |
|
31 |
5 29 30
|
sylancl |
|
32 |
|
5re |
|
33 |
32
|
a1i |
|
34 |
1 33
|
leloed |
|
35 |
|
5p1e6 |
|
36 |
35
|
breq2i |
|
37 |
36
|
a1i |
|
38 |
31 34 37
|
3bitr3rd |
|
39 |
|
4z |
|
40 |
|
zleltp1 |
|
41 |
5 39 40
|
sylancl |
|
42 |
|
4re |
|
43 |
42
|
a1i |
|
44 |
1 43
|
leloed |
|
45 |
|
4p1e5 |
|
46 |
45
|
breq2i |
|
47 |
46
|
a1i |
|
48 |
41 44 47
|
3bitr3rd |
|
49 |
|
3z |
|
50 |
|
zleltp1 |
|
51 |
5 49 50
|
sylancl |
|
52 |
|
3re |
|
53 |
52
|
a1i |
|
54 |
1 53
|
leloed |
|
55 |
|
3p1e4 |
|
56 |
55
|
breq2i |
|
57 |
56
|
a1i |
|
58 |
51 54 57
|
3bitr3rd |
|
59 |
|
eluz2 |
|
60 |
|
2re |
|
61 |
60
|
a1i |
|
62 |
|
zre |
|
63 |
61 62
|
leloed |
|
64 |
|
3m1e2 |
|
65 |
64
|
eqcomi |
|
66 |
65
|
breq1i |
|
67 |
|
zlem1lt |
|
68 |
49 67
|
mpan |
|
69 |
68
|
biimprd |
|
70 |
66 69
|
syl5bi |
|
71 |
52
|
a1i |
|
72 |
71 62
|
lenltd |
|
73 |
|
pm2.21 |
|
74 |
72 73
|
syl6bi |
|
75 |
70 74
|
syldc |
|
76 |
|
eqcom |
|
77 |
76
|
biimpi |
|
78 |
77
|
2a1d |
|
79 |
75 78
|
jaoi |
|
80 |
79
|
com12 |
|
81 |
63 80
|
sylbid |
|
82 |
81
|
imp |
|
83 |
|
2lt3 |
|
84 |
|
breq1 |
|
85 |
83 84
|
mpbiri |
|
86 |
82 85
|
impbid1 |
|
87 |
86
|
3adant1 |
|
88 |
59 87
|
sylbi |
|
89 |
88
|
orbi1d |
|
90 |
58 89
|
bitrd |
|
91 |
90
|
orbi1d |
|
92 |
48 91
|
bitrd |
|
93 |
92
|
orbi1d |
|
94 |
38 93
|
bitrd |
|
95 |
94
|
orbi1d |
|
96 |
27 95
|
bitrd |
|
97 |
96
|
orbi1d |
|
98 |
16 97
|
bitrd |
|
99 |
98
|
orbi1d |
|
100 |
99
|
biimpd |
|
101 |
4 100
|
sylbid |
|
102 |
101
|
imp |
|
103 |
|
2prm |
|
104 |
|
eleq1 |
|
105 |
103 104
|
mpbiri |
|
106 |
|
nnsum3primesprm |
|
107 |
105 106
|
syl |
|
108 |
|
3prm |
|
109 |
|
eleq1 |
|
110 |
108 109
|
mpbiri |
|
111 |
110 106
|
syl |
|
112 |
107 111
|
jaoi |
|
113 |
|
nnsum3primes4 |
|
114 |
|
eqeq1 |
|
115 |
114
|
anbi2d |
|
116 |
115
|
2rexbidv |
|
117 |
113 116
|
mpbiri |
|
118 |
112 117
|
jaoi |
|
119 |
|
5prm |
|
120 |
|
eleq1 |
|
121 |
119 120
|
mpbiri |
|
122 |
121 106
|
syl |
|
123 |
118 122
|
jaoi |
|
124 |
|
6gbe |
|
125 |
|
eleq1 |
|
126 |
124 125
|
mpbiri |
|
127 |
|
nnsum3primesgbe |
|
128 |
126 127
|
syl |
|
129 |
123 128
|
jaoi |
|
130 |
|
7prm |
|
131 |
|
eleq1 |
|
132 |
130 131
|
mpbiri |
|
133 |
132 106
|
syl |
|
134 |
129 133
|
jaoi |
|
135 |
|
8gbe |
|
136 |
|
eleq1 |
|
137 |
135 136
|
mpbiri |
|
138 |
137 127
|
syl |
|
139 |
134 138
|
jaoi |
|
140 |
102 139
|
syl |
|