Step |
Hyp |
Ref |
Expression |
1 |
|
prmreclem1.1 |
|
2 |
|
ssrab2 |
|
3 |
|
breq2 |
|
4 |
3
|
rabbidv |
|
5 |
4
|
supeq1d |
|
6 |
|
ltso |
|
7 |
6
|
supex |
|
8 |
5 1 7
|
fvmpt |
|
9 |
|
nnssz |
|
10 |
2 9
|
sstri |
|
11 |
|
oveq1 |
|
12 |
|
sq1 |
|
13 |
11 12
|
eqtrdi |
|
14 |
13
|
breq1d |
|
15 |
|
1nn |
|
16 |
15
|
a1i |
|
17 |
|
nnz |
|
18 |
|
1dvds |
|
19 |
17 18
|
syl |
|
20 |
14 16 19
|
elrabd |
|
21 |
20
|
ne0d |
|
22 |
|
nnz |
|
23 |
|
zsqcl |
|
24 |
22 23
|
syl |
|
25 |
|
id |
|
26 |
|
dvdsle |
|
27 |
24 25 26
|
syl2anr |
|
28 |
|
nnlesq |
|
29 |
28
|
adantl |
|
30 |
|
nnre |
|
31 |
30
|
adantl |
|
32 |
31
|
resqcld |
|
33 |
|
nnre |
|
34 |
33
|
adantr |
|
35 |
|
letr |
|
36 |
31 32 34 35
|
syl3anc |
|
37 |
29 36
|
mpand |
|
38 |
27 37
|
syld |
|
39 |
38
|
ralrimiva |
|
40 |
|
oveq1 |
|
41 |
40
|
breq1d |
|
42 |
41
|
ralrab |
|
43 |
39 42
|
sylibr |
|
44 |
|
brralrspcev |
|
45 |
17 43 44
|
syl2anc |
|
46 |
|
suprzcl2 |
|
47 |
10 21 45 46
|
mp3an2i |
|
48 |
8 47
|
eqeltrd |
|
49 |
2 48
|
sseldi |
|
50 |
|
oveq1 |
|
51 |
50
|
breq1d |
|
52 |
41
|
cbvrabv |
|
53 |
51 52
|
elrab2 |
|
54 |
48 53
|
sylib |
|
55 |
54
|
simprd |
|
56 |
49
|
adantr |
|
57 |
56
|
nncnd |
|
58 |
57
|
mulid1d |
|
59 |
|
eluz2gt1 |
|
60 |
59
|
adantl |
|
61 |
|
1red |
|
62 |
|
eluz2nn |
|
63 |
62
|
adantl |
|
64 |
63
|
nnred |
|
65 |
56
|
nnred |
|
66 |
56
|
nngt0d |
|
67 |
|
ltmul2 |
|
68 |
61 64 65 66 67
|
syl112anc |
|
69 |
60 68
|
mpbid |
|
70 |
58 69
|
eqbrtrrd |
|
71 |
|
nnmulcl |
|
72 |
49 62 71
|
syl2an |
|
73 |
72
|
nnred |
|
74 |
65 73
|
ltnled |
|
75 |
70 74
|
mpbid |
|
76 |
45
|
ad2antrr |
|
77 |
|
oveq1 |
|
78 |
77
|
breq1d |
|
79 |
72
|
adantr |
|
80 |
|
simpr |
|
81 |
63
|
adantr |
|
82 |
81
|
nnsqcld |
|
83 |
|
nnz |
|
84 |
82 83
|
syl |
|
85 |
49
|
nnsqcld |
|
86 |
9 85
|
sseldi |
|
87 |
85
|
nnne0d |
|
88 |
|
dvdsval2 |
|
89 |
86 87 17 88
|
syl3anc |
|
90 |
55 89
|
mpbid |
|
91 |
90
|
ad2antrr |
|
92 |
86
|
ad2antrr |
|
93 |
|
dvdscmul |
|
94 |
84 91 92 93
|
syl3anc |
|
95 |
80 94
|
mpd |
|
96 |
57
|
adantr |
|
97 |
81
|
nncnd |
|
98 |
96 97
|
sqmuld |
|
99 |
98
|
eqcomd |
|
100 |
|
nncn |
|
101 |
100
|
ad2antrr |
|
102 |
85
|
ad2antrr |
|
103 |
102
|
nncnd |
|
104 |
87
|
ad2antrr |
|
105 |
101 103 104
|
divcan2d |
|
106 |
95 99 105
|
3brtr3d |
|
107 |
78 79 106
|
elrabd |
|
108 |
|
suprzub |
|
109 |
10 76 107 108
|
mp3an2i |
|
110 |
8
|
ad2antrr |
|
111 |
109 110
|
breqtrrd |
|
112 |
75 111
|
mtand |
|
113 |
112
|
ex |
|
114 |
49 55 113
|
3jca |
|