Step |
Hyp |
Ref |
Expression |
1 |
|
elsni |
|
2 |
|
sbceq1a |
|
3 |
2
|
biimpd |
|
4 |
1 3
|
syl |
|
5 |
4
|
imdistani |
|
6 |
5
|
orcd |
|
7 |
2
|
biimprd |
|
8 |
1 7
|
syl |
|
9 |
8
|
imdistani |
|
10 |
|
noel |
|
11 |
10
|
pm2.21i |
|
12 |
11
|
adantr |
|
13 |
9 12
|
jaoi |
|
14 |
6 13
|
impbii |
|
15 |
14
|
abbii |
|
16 |
|
nfv |
|
17 |
|
nfv |
|
18 |
|
nfsbc1v |
|
19 |
17 18
|
nfan |
|
20 |
|
nfv |
|
21 |
18
|
nfn |
|
22 |
20 21
|
nfan |
|
23 |
19 22
|
nfor |
|
24 |
|
eleq1w |
|
25 |
24
|
anbi1d |
|
26 |
|
eleq1w |
|
27 |
26
|
anbi1d |
|
28 |
25 27
|
orbi12d |
|
29 |
16 23 28
|
cbvabw |
|
30 |
15 29
|
eqtri |
|
31 |
|
df-rab |
|
32 |
|
df-if |
|
33 |
30 31 32
|
3eqtr4i |
|