Step |
Hyp |
Ref |
Expression |
1 |
|
tfrlem.1 |
|
2 |
|
tfrlem.3 |
|
3 |
|
elsuci |
|
4 |
1 2
|
tfrlem10 |
|
5 |
|
fnfun |
|
6 |
4 5
|
syl |
|
7 |
|
ssun1 |
|
8 |
7 2
|
sseqtrri |
|
9 |
1
|
tfrlem9 |
|
10 |
|
funssfv |
|
11 |
10
|
3expa |
|
12 |
11
|
adantrl |
|
13 |
|
onelss |
|
14 |
13
|
imp |
|
15 |
|
fun2ssres |
|
16 |
15
|
3expa |
|
17 |
16
|
fveq2d |
|
18 |
14 17
|
sylan2 |
|
19 |
12 18
|
eqeq12d |
|
20 |
9 19
|
syl5ibr |
|
21 |
8 20
|
mpanl2 |
|
22 |
6 21
|
sylan |
|
23 |
22
|
exp32 |
|
24 |
23
|
pm2.43i |
|
25 |
24
|
pm2.43d |
|
26 |
|
opex |
|
27 |
26
|
snid |
|
28 |
|
opeq1 |
|
29 |
28
|
adantl |
|
30 |
|
eqimss |
|
31 |
8 15
|
mp3an2 |
|
32 |
6 30 31
|
syl2an |
|
33 |
|
reseq2 |
|
34 |
1
|
tfrlem6 |
|
35 |
|
resdm |
|
36 |
34 35
|
ax-mp |
|
37 |
33 36
|
eqtrdi |
|
38 |
37
|
adantl |
|
39 |
32 38
|
eqtrd |
|
40 |
39
|
fveq2d |
|
41 |
40
|
opeq2d |
|
42 |
29 41
|
eqtrd |
|
43 |
42
|
sneqd |
|
44 |
27 43
|
eleqtrid |
|
45 |
|
elun2 |
|
46 |
44 45
|
syl |
|
47 |
46 2
|
eleqtrrdi |
|
48 |
|
simpr |
|
49 |
|
sucidg |
|
50 |
49
|
adantr |
|
51 |
48 50
|
eqeltrd |
|
52 |
|
fnopfvb |
|
53 |
4 51 52
|
syl2an2r |
|
54 |
47 53
|
mpbird |
|
55 |
54
|
ex |
|
56 |
25 55
|
jaod |
|
57 |
3 56
|
syl5 |
|