Step |
Hyp |
Ref |
Expression |
1 |
|
eluzelz |
|
2 |
|
eluzelz |
|
3 |
|
zsubcl |
|
4 |
1 2 3
|
syl2an |
|
5 |
|
0z |
|
6 |
|
congid |
|
7 |
4 5 6
|
sylancl |
|
8 |
|
rmy0 |
|
9 |
|
rmy0 |
|
10 |
8 9
|
oveqan12d |
|
11 |
7 10
|
breqtrrd |
|
12 |
|
1z |
|
13 |
|
congid |
|
14 |
4 12 13
|
sylancl |
|
15 |
|
rmy1 |
|
16 |
|
rmy1 |
|
17 |
15 16
|
oveqan12d |
|
18 |
14 17
|
breqtrrd |
|
19 |
|
pm3.43 |
|
20 |
4
|
3ad2ant2 |
|
21 |
|
2z |
|
22 |
21
|
a1i |
|
23 |
|
simp2l |
|
24 |
|
nnz |
|
25 |
24
|
3ad2ant1 |
|
26 |
|
frmy |
|
27 |
26
|
fovcl |
|
28 |
23 25 27
|
syl2anc |
|
29 |
1
|
adantr |
|
30 |
29
|
3ad2ant2 |
|
31 |
28 30
|
zmulcld |
|
32 |
22 31
|
zmulcld |
|
33 |
|
simp2r |
|
34 |
26
|
fovcl |
|
35 |
33 25 34
|
syl2anc |
|
36 |
2
|
adantl |
|
37 |
36
|
3ad2ant2 |
|
38 |
35 37
|
zmulcld |
|
39 |
22 38
|
zmulcld |
|
40 |
|
peano2zm |
|
41 |
24 40
|
syl |
|
42 |
41
|
3ad2ant1 |
|
43 |
26
|
fovcl |
|
44 |
23 42 43
|
syl2anc |
|
45 |
26
|
fovcl |
|
46 |
33 42 45
|
syl2anc |
|
47 |
|
congid |
|
48 |
20 21 47
|
sylancl |
|
49 |
|
simp3r |
|
50 |
|
iddvds |
|
51 |
20 50
|
syl |
|
52 |
|
congmul |
|
53 |
20 28 35 30 37 49 51 52
|
syl322anc |
|
54 |
|
congmul |
|
55 |
20 22 22 31 38 48 53 54
|
syl322anc |
|
56 |
|
simp3l |
|
57 |
|
congsub |
|
58 |
20 32 39 44 46 55 56 57
|
syl322anc |
|
59 |
|
rmyluc |
|
60 |
23 25 59
|
syl2anc |
|
61 |
|
rmyluc |
|
62 |
33 25 61
|
syl2anc |
|
63 |
60 62
|
oveq12d |
|
64 |
58 63
|
breqtrrd |
|
65 |
64
|
3exp |
|
66 |
65
|
a2d |
|
67 |
19 66
|
syl5 |
|
68 |
|
oveq2 |
|
69 |
|
oveq2 |
|
70 |
68 69
|
oveq12d |
|
71 |
70
|
breq2d |
|
72 |
71
|
imbi2d |
|
73 |
|
oveq2 |
|
74 |
|
oveq2 |
|
75 |
73 74
|
oveq12d |
|
76 |
75
|
breq2d |
|
77 |
76
|
imbi2d |
|
78 |
|
oveq2 |
|
79 |
|
oveq2 |
|
80 |
78 79
|
oveq12d |
|
81 |
80
|
breq2d |
|
82 |
81
|
imbi2d |
|
83 |
|
oveq2 |
|
84 |
|
oveq2 |
|
85 |
83 84
|
oveq12d |
|
86 |
85
|
breq2d |
|
87 |
86
|
imbi2d |
|
88 |
|
oveq2 |
|
89 |
|
oveq2 |
|
90 |
88 89
|
oveq12d |
|
91 |
90
|
breq2d |
|
92 |
91
|
imbi2d |
|
93 |
|
oveq2 |
|
94 |
|
oveq2 |
|
95 |
93 94
|
oveq12d |
|
96 |
95
|
breq2d |
|
97 |
96
|
imbi2d |
|
98 |
11 18 67 72 77 82 87 92 97
|
2nn0ind |
|
99 |
98
|
impcom |
|
100 |
99
|
3impa |
|