Step |
Hyp |
Ref |
Expression |
1 |
|
df-iota |
|
2 |
|
abeq1 |
|
3 |
|
exdistr |
|
4 |
|
vex |
|
5 |
|
sneq |
|
6 |
5
|
eqeq2d |
|
7 |
4 6
|
ceqsexv |
|
8 |
|
snex |
|
9 |
|
eqeq1 |
|
10 |
|
eleq2 |
|
11 |
9 10
|
anbi12d |
|
12 |
|
eqcom |
|
13 |
|
velsn |
|
14 |
|
equcom |
|
15 |
13 14
|
bitri |
|
16 |
12 15
|
anbi12ci |
|
17 |
11 16
|
syl6bb |
|
18 |
8 17
|
ceqsexv |
|
19 |
|
an13 |
|
20 |
19
|
exbii |
|
21 |
18 20
|
bitr3i |
|
22 |
21
|
exbii |
|
23 |
7 22
|
bitr3i |
|
24 |
|
excom |
|
25 |
23 24
|
bitri |
|
26 |
|
eluniab |
|
27 |
3 25 26
|
3bitr4i |
|
28 |
2 27
|
mpgbir |
|
29 |
|
df-sn |
|
30 |
|
dfsingles2 |
|
31 |
29 30
|
ineq12i |
|
32 |
|
inab |
|
33 |
|
19.42v |
|
34 |
33
|
bicomi |
|
35 |
34
|
abbii |
|
36 |
32 35
|
eqtri |
|
37 |
31 36
|
eqtri |
|
38 |
37
|
unieqi |
|
39 |
28 38
|
eqtr4i |
|
40 |
39
|
unieqi |
|
41 |
1 40
|
eqtri |
|