Step |
Hyp |
Ref |
Expression |
1 |
|
dfef2.1 |
|
2 |
|
dfef2.2 |
|
3 |
|
dfef2.3 |
|
4 |
|
ax-1cn |
|
5 |
|
simpl |
|
6 |
|
nncn |
|
7 |
6
|
adantl |
|
8 |
|
nnne0 |
|
9 |
8
|
adantl |
|
10 |
5 7 9
|
divcld |
|
11 |
|
addcl |
|
12 |
4 10 11
|
sylancr |
|
13 |
|
nnnn0 |
|
14 |
13
|
adantl |
|
15 |
|
cxpexp |
|
16 |
12 14 15
|
syl2anc |
|
17 |
16
|
mpteq2dva |
|
18 |
|
nnrp |
|
19 |
18
|
ssriv |
|
20 |
19
|
a1i |
|
21 |
|
eqid |
|
22 |
21
|
efrlim |
|
23 |
20 22
|
rlimres2 |
|
24 |
17 23
|
eqbrtrrd |
|
25 |
|
nnuz |
|
26 |
|
1zzd |
|
27 |
12 14
|
expcld |
|
28 |
27
|
fmpttd |
|
29 |
25 26 28
|
rlimclim |
|
30 |
24 29
|
mpbid |
|
31 |
2 30
|
syl |
|
32 |
|
nnex |
|
33 |
32
|
mptex |
|
34 |
33
|
a1i |
|
35 |
|
1zzd |
|
36 |
|
oveq2 |
|
37 |
36
|
oveq2d |
|
38 |
|
id |
|
39 |
37 38
|
oveq12d |
|
40 |
|
eqid |
|
41 |
|
ovex |
|
42 |
39 40 41
|
fvmpt |
|
43 |
42
|
adantl |
|
44 |
43 3
|
eqtr4d |
|
45 |
25 34 1 35 44
|
climeq |
|
46 |
31 45
|
mpbid |
|