Step |
Hyp |
Ref |
Expression |
1 |
|
nfdisj1 |
|
2 |
|
nfcv |
|
3 |
|
nfv |
|
4 |
|
nfcsb1v |
|
5 |
4
|
nfcri |
|
6 |
3 5
|
nfan |
|
7 |
6
|
nfab |
|
8 |
7
|
nfuni |
|
9 |
8
|
nfcsb1 |
|
10 |
9
|
nfeq1 |
|
11 |
2 10
|
nfralw |
|
12 |
|
eqeq2 |
|
13 |
12
|
raleqbi1dv |
|
14 |
|
vex |
|
15 |
14
|
a1i |
|
16 |
|
simplll |
|
17 |
|
simpllr |
|
18 |
|
simprl |
|
19 |
|
simplr |
|
20 |
|
simprr |
|
21 |
|
csbeq1a |
|
22 |
4 21
|
disjif |
|
23 |
16 17 18 19 20 22
|
syl122anc |
|
24 |
|
simpr |
|
25 |
|
simpllr |
|
26 |
24 25
|
eqeltrrd |
|
27 |
|
simplr |
|
28 |
21
|
eleq2d |
|
29 |
24 28
|
syl |
|
30 |
27 29
|
mpbid |
|
31 |
26 30
|
jca |
|
32 |
23 31
|
impbida |
|
33 |
|
equcom |
|
34 |
32 33
|
syl6bb |
|
35 |
34
|
abbidv |
|
36 |
|
df-sn |
|
37 |
35 36
|
eqtr4di |
|
38 |
37
|
unieqd |
|
39 |
|
vex |
|
40 |
39
|
unisn |
|
41 |
38 40
|
eqtrdi |
|
42 |
|
csbeq1 |
|
43 |
|
csbid |
|
44 |
42 43
|
eqtrdi |
|
45 |
41 44
|
syl |
|
46 |
45
|
ralrimiva |
|
47 |
1 11 13 15 46
|
elabreximd |
|
48 |
47
|
ralrimiva |
|
49 |
|
invdisj |
|
50 |
48 49
|
syl |
|