Step |
Hyp |
Ref |
Expression |
1 |
|
df-3 |
|
2 |
1
|
fveq2i |
|
3 |
|
2nn0 |
|
4 |
|
ackvalsuc1mpt |
|
5 |
3 4
|
ax-mp |
|
6 |
|
peano2nn0 |
|
7 |
|
3nn0 |
|
8 |
|
ackval2 |
|
9 |
8
|
itcovalt2 |
|
10 |
6 7 9
|
sylancl |
|
11 |
10
|
fveq1d |
|
12 |
|
eqidd |
|
13 |
|
oveq1 |
|
14 |
|
3cn |
|
15 |
|
ax-1cn |
|
16 |
|
3p1e4 |
|
17 |
14 15 16
|
addcomli |
|
18 |
13 17
|
eqtrdi |
|
19 |
18
|
oveq1d |
|
20 |
19
|
oveq1d |
|
21 |
20
|
adantl |
|
22 |
|
1nn0 |
|
23 |
22
|
a1i |
|
24 |
|
ovexd |
|
25 |
12 21 23 24
|
fvmptd |
|
26 |
|
sq2 |
|
27 |
26
|
eqcomi |
|
28 |
27
|
a1i |
|
29 |
28
|
oveq1d |
|
30 |
|
2cnd |
|
31 |
3
|
a1i |
|
32 |
30 6 31
|
expaddd |
|
33 |
|
nn0cn |
|
34 |
|
1cnd |
|
35 |
30 33 34
|
add12d |
|
36 |
|
2p1e3 |
|
37 |
36
|
oveq2i |
|
38 |
35 37
|
eqtrdi |
|
39 |
38
|
oveq2d |
|
40 |
29 32 39
|
3eqtr2d |
|
41 |
40
|
oveq1d |
|
42 |
11 25 41
|
3eqtrd |
|
43 |
42
|
mpteq2ia |
|
44 |
2 5 43
|
3eqtri |
|