Step |
Hyp |
Ref |
Expression |
1 |
|
disjabrexf.1 |
|
2 |
|
nfdisj1 |
|
3 |
|
nfcv |
|
4 |
1
|
nfcri |
|
5 |
|
nfcsb1v |
|
6 |
5
|
nfcri |
|
7 |
4 6
|
nfan |
|
8 |
7
|
nfab |
|
9 |
8
|
nfuni |
|
10 |
9
|
nfcsb1 |
|
11 |
10
|
nfeq1 |
|
12 |
3 11
|
nfralw |
|
13 |
|
eqeq2 |
|
14 |
13
|
raleqbi1dv |
|
15 |
|
vex |
|
16 |
15
|
a1i |
|
17 |
|
simplll |
|
18 |
|
simpllr |
|
19 |
|
simprl |
|
20 |
|
simplr |
|
21 |
|
simprr |
|
22 |
|
csbeq1a |
|
23 |
1 5 22
|
disjif2 |
|
24 |
17 18 19 20 21 23
|
syl122anc |
|
25 |
|
simpr |
|
26 |
|
simpllr |
|
27 |
25 26
|
eqeltrrd |
|
28 |
|
simplr |
|
29 |
22
|
eleq2d |
|
30 |
25 29
|
syl |
|
31 |
28 30
|
mpbid |
|
32 |
27 31
|
jca |
|
33 |
24 32
|
impbida |
|
34 |
|
equcom |
|
35 |
33 34
|
syl6bb |
|
36 |
35
|
abbidv |
|
37 |
|
df-sn |
|
38 |
36 37
|
eqtr4di |
|
39 |
38
|
unieqd |
|
40 |
|
vex |
|
41 |
40
|
unisn |
|
42 |
39 41
|
eqtrdi |
|
43 |
|
csbeq1 |
|
44 |
|
csbid |
|
45 |
43 44
|
eqtrdi |
|
46 |
42 45
|
syl |
|
47 |
46
|
ralrimiva |
|
48 |
2 12 14 16 47
|
elabreximd |
|
49 |
48
|
ralrimiva |
|
50 |
|
invdisj |
|
51 |
49 50
|
syl |
|