Step |
Hyp |
Ref |
Expression |
1 |
|
simprl |
|
2 |
|
limsuc |
|
3 |
2
|
ad2antrr |
|
4 |
1 3
|
mpbid |
|
5 |
|
simprr |
|
6 |
|
limord |
|
7 |
|
elex |
|
8 |
6 7
|
anim12i |
|
9 |
|
elon2 |
|
10 |
8 9
|
sylibr |
|
11 |
|
onelon |
|
12 |
10 1 11
|
syl2an2r |
|
13 |
|
madeoldsuc |
|
14 |
12 13
|
syl |
|
15 |
5 14
|
eleqtrd |
|
16 |
|
fveq2 |
|
17 |
16
|
eleq2d |
|
18 |
17
|
rspcev |
|
19 |
4 15 18
|
syl2anc |
|
20 |
19
|
expr |
|
21 |
20
|
rexlimdva |
|
22 |
|
simprl |
|
23 |
|
onelon |
|
24 |
10 22 23
|
syl2an2r |
|
25 |
|
oldssmade |
|
26 |
24 25
|
syl |
|
27 |
|
simprr |
|
28 |
26 27
|
sseldd |
|
29 |
|
fveq2 |
|
30 |
29
|
eleq2d |
|
31 |
30
|
rspcev |
|
32 |
22 28 31
|
syl2anc |
|
33 |
32
|
expr |
|
34 |
33
|
rexlimdva |
|
35 |
21 34
|
impbid |
|
36 |
|
elold |
|
37 |
10 36
|
syl |
|
38 |
|
eliun |
|
39 |
38
|
a1i |
|
40 |
35 37 39
|
3bitr4d |
|
41 |
40
|
eqrdv |
|
42 |
|
oldf |
|
43 |
|
ffun |
|
44 |
|
funiunfv |
|
45 |
42 43 44
|
mp2b |
|
46 |
41 45
|
eqtrdi |
|