Step |
Hyp |
Ref |
Expression |
1 |
|
lcmineqlem1.1 |
|
2 |
|
lcmineqlem1.2 |
|
3 |
|
lcmineqlem1.3 |
|
4 |
|
lcmineqlem1.4 |
|
5 |
|
elunitcn |
|
6 |
|
ax-1cn |
|
7 |
|
negsub |
|
8 |
6 7
|
mpan |
|
9 |
8
|
oveq1d |
|
10 |
9
|
adantl |
|
11 |
|
negcl |
|
12 |
|
1cnd |
|
13 |
3
|
nnnn0d |
|
14 |
2
|
nnnn0d |
|
15 |
|
nn0sub |
|
16 |
13 14 15
|
syl2anc |
|
17 |
4 16
|
mpbid |
|
18 |
|
binom |
|
19 |
18
|
3com23 |
|
20 |
19
|
3expia |
|
21 |
12 17 20
|
syl2anc |
|
22 |
11 21
|
syl5 |
|
23 |
22
|
imp |
|
24 |
10 23
|
eqtr3d |
|
25 |
|
elfzelz |
|
26 |
2
|
nnzd |
|
27 |
3
|
nnzd |
|
28 |
|
zsubcl |
|
29 |
26 27 28
|
syl2anc |
|
30 |
|
zsubcl |
|
31 |
29 30
|
sylan |
|
32 |
25 31
|
sylan2 |
|
33 |
|
1exp |
|
34 |
32 33
|
syl |
|
35 |
34
|
3adant2 |
|
36 |
35
|
oveq1d |
|
37 |
11
|
3ad2ant2 |
|
38 |
|
elfznn0 |
|
39 |
38
|
3ad2ant3 |
|
40 |
|
expcl |
|
41 |
37 39 40
|
syl2anc |
|
42 |
41
|
mulid2d |
|
43 |
36 42
|
eqtrd |
|
44 |
|
mulm1 |
|
45 |
44
|
oveq1d |
|
46 |
45
|
3ad2ant2 |
|
47 |
43 46
|
eqtr4d |
|
48 |
|
neg1cn |
|
49 |
|
mulexp |
|
50 |
48 49
|
mp3an1 |
|
51 |
38 50
|
sylan2 |
|
52 |
51
|
3adant1 |
|
53 |
47 52
|
eqtrd |
|
54 |
53
|
oveq2d |
|
55 |
|
bccl |
|
56 |
17 25 55
|
syl2an |
|
57 |
56
|
3adant2 |
|
58 |
57
|
nn0cnd |
|
59 |
|
expcl |
|
60 |
48 39 59
|
sylancr |
|
61 |
|
expcl |
|
62 |
38 61
|
sylan2 |
|
63 |
62
|
3adant1 |
|
64 |
58 60 63
|
mulassd |
|
65 |
54 64
|
eqtr4d |
|
66 |
58 60
|
mulcomd |
|
67 |
66
|
oveq1d |
|
68 |
65 67
|
eqtrd |
|
69 |
68
|
3expa |
|
70 |
69
|
sumeq2dv |
|
71 |
24 70
|
eqtrd |
|
72 |
5 71
|
sylan2 |
|
73 |
72
|
oveq2d |
|
74 |
73
|
itgeq2dv |
|
75 |
1 74
|
syl5eq |
|