Step |
Hyp |
Ref |
Expression |
1 |
|
expgrowthi.s |
|
2 |
|
expgrowthi.k |
|
3 |
|
expgrowthi.y0 |
|
4 |
|
expgrowthi.yt |
|
5 |
|
oveq2 |
|
6 |
5
|
fveq2d |
|
7 |
6
|
oveq2d |
|
8 |
7
|
cbvmptv |
|
9 |
4 8
|
eqtri |
|
10 |
9
|
oveq2i |
|
11 |
|
elpri |
|
12 |
|
eleq2 |
|
13 |
|
recn |
|
14 |
12 13
|
syl6bi |
|
15 |
|
eleq2 |
|
16 |
15
|
biimpd |
|
17 |
14 16
|
jaoi |
|
18 |
1 11 17
|
3syl |
|
19 |
18
|
imp |
|
20 |
|
mulcl |
|
21 |
2 20
|
sylan |
|
22 |
|
efcl |
|
23 |
21 22
|
syl |
|
24 |
19 23
|
syldan |
|
25 |
|
ovexd |
|
26 |
|
cnelprrecn |
|
27 |
26
|
a1i |
|
28 |
19 21
|
syldan |
|
29 |
2
|
adantr |
|
30 |
|
efcl |
|
31 |
30
|
adantl |
|
32 |
|
1cnd |
|
33 |
1
|
dvmptid |
|
34 |
1 19 32 33 2
|
dvmptcmul |
|
35 |
2
|
mulid1d |
|
36 |
35
|
mpteq2dv |
|
37 |
34 36
|
eqtrd |
|
38 |
|
dvef |
|
39 |
|
eff |
|
40 |
|
ffn |
|
41 |
39 40
|
ax-mp |
|
42 |
|
dffn5 |
|
43 |
41 42
|
mpbi |
|
44 |
43
|
oveq2i |
|
45 |
38 44 43
|
3eqtr3i |
|
46 |
45
|
a1i |
|
47 |
|
fveq2 |
|
48 |
1 27 28 29 31 31 37 46 47 47
|
dvmptco |
|
49 |
|
mulcom |
|
50 |
24 2 49
|
syl2anr |
|
51 |
50
|
anabss5 |
|
52 |
51
|
mpteq2dva |
|
53 |
48 52
|
eqtrd |
|
54 |
1 24 25 53 3
|
dvmptcmul |
|
55 |
3 2 24
|
3anim123i |
|
56 |
55
|
3anidm12 |
|
57 |
56
|
anabss5 |
|
58 |
|
mul12 |
|
59 |
57 58
|
syl |
|
60 |
59
|
mpteq2dva |
|
61 |
54 60
|
eqtrd |
|
62 |
10 61
|
syl5eq |
|
63 |
|
ovexd |
|
64 |
|
fconstmpt |
|
65 |
64
|
a1i |
|
66 |
9
|
a1i |
|
67 |
1 29 63 65 66
|
offval2 |
|
68 |
62 67
|
eqtr4d |
|