Step |
Hyp |
Ref |
Expression |
1 |
|
finxpreclem3.1 |
|
2 |
|
df-ov |
|
3 |
1
|
a1i |
|
4 |
|
eqeq1 |
|
5 |
|
eleq1 |
|
6 |
4 5
|
bi2anan9 |
|
7 |
|
eleq1 |
|
8 |
7
|
adantl |
|
9 |
|
unieq |
|
10 |
9
|
adantr |
|
11 |
|
fveq2 |
|
12 |
11
|
adantl |
|
13 |
10 12
|
opeq12d |
|
14 |
|
opeq12 |
|
15 |
8 13 14
|
ifbieq12d |
|
16 |
6 15
|
ifbieq2d |
|
17 |
|
sssucid |
|
18 |
|
df-2o |
|
19 |
17 18
|
sseqtrri |
|
20 |
|
1on |
|
21 |
18 20
|
sucneqoni |
|
22 |
21
|
necomi |
|
23 |
|
df-pss |
|
24 |
19 22 23
|
mpbir2an |
|
25 |
|
ssnpss |
|
26 |
24 25
|
mt2 |
|
27 |
|
sseq2 |
|
28 |
26 27
|
mtbiri |
|
29 |
28
|
con2i |
|
30 |
29
|
intnanrd |
|
31 |
30
|
iffalsed |
|
32 |
|
iftrue |
|
33 |
31 32
|
sylan9eq |
|
34 |
16 33
|
sylan9eqr |
|
35 |
34
|
adantlll |
|
36 |
|
simpll |
|
37 |
|
elex |
|
38 |
37
|
adantl |
|
39 |
|
opex |
|
40 |
39
|
a1i |
|
41 |
3 35 36 38 40
|
ovmpod |
|
42 |
2 41
|
syl5reqr |
|