Step |
Hyp |
Ref |
Expression |
1 |
|
lencl |
|
2 |
|
nn0cn |
|
3 |
|
peano2cnm |
|
4 |
3
|
subid1d |
|
5 |
4
|
oveq1d |
|
6 |
|
sub1m1 |
|
7 |
5 6
|
eqtrd |
|
8 |
1 2 7
|
3syl |
|
9 |
8
|
adantr |
|
10 |
9
|
oveq2d |
|
11 |
10
|
raleqdv |
|
12 |
11
|
biimpcd |
|
13 |
12
|
adantr |
|
14 |
13
|
adantl |
|
15 |
14
|
impcom |
|
16 |
|
lsw |
|
17 |
|
2m1e1 |
|
18 |
17
|
a1i |
|
19 |
18
|
eqcomd |
|
20 |
19
|
oveq2d |
|
21 |
1 2
|
syl |
|
22 |
|
2cnd |
|
23 |
|
1cnd |
|
24 |
21 22 23
|
subsubd |
|
25 |
20 24
|
eqtrd |
|
26 |
25
|
fveq2d |
|
27 |
16 26
|
eqtrd |
|
28 |
27
|
adantr |
|
29 |
28
|
adantr |
|
30 |
|
eqeq1 |
|
31 |
30
|
adantl |
|
32 |
29 31
|
mpbid |
|
33 |
32
|
preq2d |
|
34 |
33
|
eleq1d |
|
35 |
34
|
biimpd |
|
36 |
35
|
ex |
|
37 |
36
|
com13 |
|
38 |
37
|
adantl |
|
39 |
38
|
impcom |
|
40 |
39
|
impcom |
|
41 |
|
ovexd |
|
42 |
|
fveq2 |
|
43 |
|
fvoveq1 |
|
44 |
42 43
|
preq12d |
|
45 |
44
|
eleq1d |
|
46 |
45
|
ralunsn |
|
47 |
41 46
|
syl |
|
48 |
15 40 47
|
mpbir2and |
|
49 |
|
1e2m1 |
|
50 |
49
|
a1i |
|
51 |
50
|
oveq2d |
|
52 |
51 24
|
eqtrd |
|
53 |
52
|
oveq2d |
|
54 |
53
|
adantr |
|
55 |
|
nn0re |
|
56 |
|
2re |
|
57 |
56
|
a1i |
|
58 |
55 57
|
subge0d |
|
59 |
58
|
biimprd |
|
60 |
|
nn0z |
|
61 |
|
2z |
|
62 |
61
|
a1i |
|
63 |
60 62
|
zsubcld |
|
64 |
59 63
|
jctild |
|
65 |
1 64
|
syl |
|
66 |
65
|
imp |
|
67 |
|
elnn0z |
|
68 |
66 67
|
sylibr |
|
69 |
|
elnn0uz |
|
70 |
68 69
|
sylib |
|
71 |
|
fzosplitsn |
|
72 |
70 71
|
syl |
|
73 |
54 72
|
eqtrd |
|
74 |
73
|
adantr |
|
75 |
74
|
raleqdv |
|
76 |
48 75
|
mpbird |
|
77 |
76
|
ex |
|