Step |
Hyp |
Ref |
Expression |
1 |
|
eluzge2nn0 |
|
2 |
|
nn0eo |
|
3 |
1 2
|
syl |
|
4 |
|
dignn0ehalf |
|
5 |
1 4
|
syl3an2 |
|
6 |
|
eluzelz |
|
7 |
|
nn0z |
|
8 |
|
zefldiv2 |
|
9 |
6 7 8
|
syl2anr |
|
10 |
9
|
eqcomd |
|
11 |
10
|
3adant3 |
|
12 |
11
|
oveq2d |
|
13 |
5 12
|
eqtrd |
|
14 |
13
|
3exp |
|
15 |
6
|
3ad2ant2 |
|
16 |
|
simp2 |
|
17 |
|
simp1 |
|
18 |
|
nno |
|
19 |
16 17 18
|
syl2anc |
|
20 |
|
simp3 |
|
21 |
|
dignn0flhalflem2 |
|
22 |
15 19 20 21
|
syl3anc |
|
23 |
22
|
oveq1d |
|
24 |
|
2nn |
|
25 |
24
|
a1i |
|
26 |
|
peano2nn0 |
|
27 |
26
|
3ad2ant3 |
|
28 |
|
nn0rp0 |
|
29 |
1 28
|
syl |
|
30 |
29
|
3ad2ant2 |
|
31 |
|
nn0digval |
|
32 |
25 27 30 31
|
syl3anc |
|
33 |
|
eluzelre |
|
34 |
33
|
rehalfcld |
|
35 |
1
|
nn0ge0d |
|
36 |
|
2re |
|
37 |
|
2pos |
|
38 |
36 37
|
pm3.2i |
|
39 |
38
|
a1i |
|
40 |
|
divge0 |
|
41 |
33 35 39 40
|
syl21anc |
|
42 |
|
flge0nn0 |
|
43 |
34 41 42
|
syl2anc |
|
44 |
43
|
3ad2ant2 |
|
45 |
|
nn0rp0 |
|
46 |
44 45
|
syl |
|
47 |
|
nn0digval |
|
48 |
25 20 46 47
|
syl3anc |
|
49 |
23 32 48
|
3eqtr4d |
|
50 |
49
|
3exp |
|
51 |
14 50
|
jaoi |
|
52 |
3 51
|
mpcom |
|
53 |
52
|
imp |
|