Step |
Hyp |
Ref |
Expression |
1 |
|
brapply.1 |
|
2 |
|
brapply.2 |
|
3 |
|
brapply.3 |
|
4 |
|
snex |
|
5 |
4
|
inex1 |
|
6 |
|
unieq |
|
7 |
6
|
unieqd |
|
8 |
7
|
eqeq2d |
|
9 |
5 8
|
ceqsexv |
|
10 |
|
df-apply |
|
11 |
10
|
breqi |
|
12 |
|
opex |
|
13 |
12 3
|
brco |
|
14 |
|
vex |
|
15 |
12 14
|
brco |
|
16 |
|
vex |
|
17 |
12 16
|
brco |
|
18 |
|
vex |
|
19 |
1 2 18
|
brpprod3a |
|
20 |
|
3anrot |
|
21 |
|
vex |
|
22 |
21
|
ideq |
|
23 |
|
eqcom |
|
24 |
22 23
|
bitri |
|
25 |
|
vex |
|
26 |
2 25
|
brsingle |
|
27 |
|
biid |
|
28 |
24 26 27
|
3anbi123i |
|
29 |
20 28
|
bitri |
|
30 |
29
|
2exbii |
|
31 |
|
snex |
|
32 |
|
opeq1 |
|
33 |
32
|
eqeq2d |
|
34 |
|
opeq2 |
|
35 |
34
|
eqeq2d |
|
36 |
1 31 33 35
|
ceqsex2v |
|
37 |
19 30 36
|
3bitri |
|
38 |
37
|
anbi1i |
|
39 |
38
|
exbii |
|
40 |
|
opex |
|
41 |
|
breq1 |
|
42 |
40 41
|
ceqsexv |
|
43 |
40 16
|
brco |
|
44 |
1 31 14
|
brimg |
|
45 |
14 16
|
brsingle |
|
46 |
44 45
|
anbi12i |
|
47 |
46
|
exbii |
|
48 |
1
|
imaex |
|
49 |
|
sneq |
|
50 |
49
|
eqeq2d |
|
51 |
48 50
|
ceqsexv |
|
52 |
47 51
|
bitri |
|
53 |
42 43 52
|
3bitri |
|
54 |
17 39 53
|
3bitri |
|
55 |
|
eqid |
|
56 |
|
brxp |
|
57 |
16 14 56
|
mpbir2an |
|
58 |
|
epel |
|
59 |
58
|
anbi1ci |
|
60 |
16
|
brresi |
|
61 |
|
elin |
|
62 |
59 60 61
|
3bitr4ri |
|
63 |
16 14 55 57 62
|
brtxpsd3 |
|
64 |
54 63
|
anbi12i |
|
65 |
64
|
exbii |
|
66 |
|
ineq1 |
|
67 |
66
|
eqeq2d |
|
68 |
4 67
|
ceqsexv |
|
69 |
15 65 68
|
3bitri |
|
70 |
14 3
|
brco |
|
71 |
16
|
brbigcup |
|
72 |
|
eqcom |
|
73 |
71 72
|
bitri |
|
74 |
3
|
brbigcup |
|
75 |
|
eqcom |
|
76 |
74 75
|
bitri |
|
77 |
73 76
|
anbi12i |
|
78 |
77
|
exbii |
|
79 |
|
vuniex |
|
80 |
|
unieq |
|
81 |
80
|
eqeq2d |
|
82 |
79 81
|
ceqsexv |
|
83 |
70 78 82
|
3bitri |
|
84 |
69 83
|
anbi12i |
|
85 |
84
|
exbii |
|
86 |
11 13 85
|
3bitri |
|
87 |
|
dffv5 |
|
88 |
87
|
eqeq2i |
|
89 |
9 86 88
|
3bitr4i |
|