Step |
Hyp |
Ref |
Expression |
1 |
|
opiota.1 |
|
2 |
|
opiota.2 |
|
3 |
|
opiota.3 |
|
4 |
|
opiota.4 |
|
5 |
|
opiota.5 |
|
6 |
4 5
|
ceqsrex2v |
|
7 |
6
|
bicomd |
|
8 |
|
opex |
|
9 |
8
|
a1i |
|
10 |
|
id |
|
11 |
|
eqeq1 |
|
12 |
|
eqcom |
|
13 |
|
vex |
|
14 |
|
vex |
|
15 |
13 14
|
opth |
|
16 |
12 15
|
bitri |
|
17 |
11 16
|
bitrdi |
|
18 |
17
|
anbi1d |
|
19 |
18
|
2rexbidv |
|
20 |
19
|
adantl |
|
21 |
|
nfeu1 |
|
22 |
|
nfvd |
|
23 |
|
nfcvd |
|
24 |
9 10 20 21 22 23
|
iota2df |
|
25 |
|
eqcom |
|
26 |
1
|
eqeq1i |
|
27 |
25 26
|
bitri |
|
28 |
24 27
|
bitr4di |
|
29 |
7 28
|
sylan9bbr |
|
30 |
29
|
pm5.32da |
|
31 |
|
opelxpi |
|
32 |
|
simpl |
|
33 |
32
|
eleq1d |
|
34 |
31 33
|
syl5ibrcom |
|
35 |
34
|
rexlimivv |
|
36 |
35
|
abssi |
|
37 |
|
iotacl |
|
38 |
36 37
|
sseldi |
|
39 |
1 38
|
eqeltrid |
|
40 |
|
opelxp |
|
41 |
|
eleq1 |
|
42 |
40 41
|
bitr3id |
|
43 |
39 42
|
syl5ibrcom |
|
44 |
43
|
pm4.71rd |
|
45 |
|
1st2nd2 |
|
46 |
39 45
|
syl |
|
47 |
46
|
eqeq2d |
|
48 |
30 44 47
|
3bitr2d |
|
49 |
|
df-3an |
|
50 |
2
|
eqeq2i |
|
51 |
3
|
eqeq2i |
|
52 |
50 51
|
anbi12i |
|
53 |
|
fvex |
|
54 |
|
fvex |
|
55 |
53 54
|
opth2 |
|
56 |
52 55
|
bitr4i |
|
57 |
48 49 56
|
3bitr4g |
|