Step |
Hyp |
Ref |
Expression |
1 |
|
peano5uzi.1 |
|
2 |
|
breq2 |
|
3 |
2
|
elrab |
|
4 |
|
zcn |
|
5 |
4
|
ad2antrl |
|
6 |
|
zcn |
|
7 |
1 6
|
ax-mp |
|
8 |
|
ax-1cn |
|
9 |
7 8
|
subcli |
|
10 |
|
npcan |
|
11 |
5 9 10
|
sylancl |
|
12 |
|
subsub |
|
13 |
7 8 12
|
mp3an23 |
|
14 |
5 13
|
syl |
|
15 |
|
znn0sub |
|
16 |
1 15
|
mpan |
|
17 |
16
|
biimpa |
|
18 |
17
|
adantl |
|
19 |
|
nn0p1nn |
|
20 |
18 19
|
syl |
|
21 |
14 20
|
eqeltrd |
|
22 |
|
simpl |
|
23 |
|
oveq1 |
|
24 |
23
|
eleq1d |
|
25 |
24
|
imbi2d |
|
26 |
|
oveq1 |
|
27 |
26
|
eleq1d |
|
28 |
27
|
imbi2d |
|
29 |
|
oveq1 |
|
30 |
29
|
eleq1d |
|
31 |
30
|
imbi2d |
|
32 |
|
oveq1 |
|
33 |
32
|
eleq1d |
|
34 |
33
|
imbi2d |
|
35 |
8 7
|
pncan3i |
|
36 |
|
simpl |
|
37 |
35 36
|
eqeltrid |
|
38 |
|
oveq1 |
|
39 |
38
|
eleq1d |
|
40 |
39
|
rspccv |
|
41 |
40
|
ad2antll |
|
42 |
|
nncn |
|
43 |
42
|
adantr |
|
44 |
|
add32 |
|
45 |
9 8 44
|
mp3an23 |
|
46 |
43 45
|
syl |
|
47 |
46
|
eleq1d |
|
48 |
41 47
|
sylibd |
|
49 |
48
|
ex |
|
50 |
49
|
a2d |
|
51 |
25 28 31 34 37 50
|
nnind |
|
52 |
21 22 51
|
sylc |
|
53 |
11 52
|
eqeltrrd |
|
54 |
53
|
ex |
|
55 |
3 54
|
syl5bi |
|
56 |
55
|
ssrdv |
|