Step |
Hyp |
Ref |
Expression |
1 |
|
peano2 |
|
2 |
|
nnon |
|
3 |
1 2
|
syl |
|
4 |
|
omv |
|
5 |
3 4
|
sylan2 |
|
6 |
1
|
adantl |
|
7 |
6
|
fvresd |
|
8 |
5 7
|
eqtr4d |
|
9 |
|
ovex |
|
10 |
|
oveq1 |
|
11 |
|
eqid |
|
12 |
|
ovex |
|
13 |
10 11 12
|
fvmpt |
|
14 |
9 13
|
ax-mp |
|
15 |
|
nnon |
|
16 |
|
omv |
|
17 |
15 16
|
sylan2 |
|
18 |
|
fvres |
|
19 |
18
|
adantl |
|
20 |
17 19
|
eqtr4d |
|
21 |
20
|
fveq2d |
|
22 |
14 21
|
eqtr3id |
|
23 |
|
frsuc |
|
24 |
23
|
adantl |
|
25 |
22 24
|
eqtr4d |
|
26 |
8 25
|
eqtr4d |
|