Step |
Hyp |
Ref |
Expression |
1 |
|
oveq2 |
|
2 |
1
|
eleq1d |
|
3 |
2
|
imbi2d |
|
4 |
|
oveq2 |
|
5 |
4
|
eleq1d |
|
6 |
|
oveq2 |
|
7 |
6
|
eleq1d |
|
8 |
|
oveq2 |
|
9 |
8
|
eleq1d |
|
10 |
|
nnon |
|
11 |
|
oe0 |
|
12 |
10 11
|
syl |
|
13 |
|
df-1o |
|
14 |
|
peano1 |
|
15 |
|
peano2 |
|
16 |
14 15
|
ax-mp |
|
17 |
13 16
|
eqeltri |
|
18 |
12 17
|
eqeltrdi |
|
19 |
|
nnmcl |
|
20 |
19
|
expcom |
|
21 |
20
|
adantr |
|
22 |
|
nnesuc |
|
23 |
22
|
eleq1d |
|
24 |
21 23
|
sylibrd |
|
25 |
24
|
expcom |
|
26 |
5 7 9 18 25
|
finds2 |
|
27 |
3 26
|
vtoclga |
|
28 |
27
|
impcom |
|