Step |
Hyp |
Ref |
Expression |
1 |
|
eqss |
|
2 |
1
|
a1i |
|
3 |
|
unss |
|
4 |
3
|
bicomi |
|
5 |
4
|
a1i |
|
6 |
|
elun |
|
7 |
|
snssg |
|
8 |
|
snssg |
|
9 |
7 8
|
orbi12d |
|
10 |
6 9
|
syl5rbb |
|
11 |
|
snssg |
|
12 |
10 11
|
bitr2d |
|
13 |
5 12
|
anbi12d |
|
14 |
|
or3or |
|
15 |
14
|
anbi2i |
|
16 |
|
andi3or |
|
17 |
15 16
|
bitri |
|
18 |
|
an4 |
|
19 |
|
eqss |
|
20 |
|
eqss |
|
21 |
19 20
|
anbi12i |
|
22 |
21
|
bicomi |
|
23 |
18 22
|
bitri |
|
24 |
23
|
a1i |
|
25 |
|
an4 |
|
26 |
19
|
bicomi |
|
27 |
26
|
a1i |
|
28 |
|
sssn |
|
29 |
28
|
a1i |
|
30 |
29
|
anbi1d |
|
31 |
|
andir |
|
32 |
|
n0i |
|
33 |
8 32
|
syl6bir |
|
34 |
33
|
con2d |
|
35 |
34
|
pm4.71d |
|
36 |
|
eqimss2 |
|
37 |
|
iman |
|
38 |
36 37
|
mpbi |
|
39 |
38
|
biorfi |
|
40 |
35 39
|
bitr2di |
|
41 |
31 40
|
syl5bb |
|
42 |
30 41
|
bitrd |
|
43 |
27 42
|
anbi12d |
|
44 |
25 43
|
syl5bb |
|
45 |
|
an4 |
|
46 |
|
sssn |
|
47 |
46
|
a1i |
|
48 |
47
|
anbi1d |
|
49 |
|
andir |
|
50 |
|
n0i |
|
51 |
7 50
|
syl6bir |
|
52 |
51
|
con2d |
|
53 |
52
|
pm4.71d |
|
54 |
|
eqimss2 |
|
55 |
|
iman |
|
56 |
54 55
|
mpbi |
|
57 |
56
|
biorfi |
|
58 |
53 57
|
bitr2di |
|
59 |
49 58
|
syl5bb |
|
60 |
48 59
|
bitrd |
|
61 |
20
|
bicomi |
|
62 |
61
|
a1i |
|
63 |
60 62
|
anbi12d |
|
64 |
45 63
|
syl5bb |
|
65 |
24 44 64
|
3orbi123d |
|
66 |
17 65
|
syl5bb |
|
67 |
2 13 66
|
3bitrd |
|
68 |
|
snprc |
|
69 |
68
|
biimpi |
|
70 |
69
|
eqeq2d |
|
71 |
|
pm4.25 |
|
72 |
71
|
orbi1i |
|
73 |
71 72
|
bitri |
|
74 |
69
|
eqeq2d |
|
75 |
69
|
eqeq2d |
|
76 |
74 75
|
anbi12d |
|
77 |
74
|
anbi1d |
|
78 |
76 77
|
orbi12d |
|
79 |
75
|
anbi2d |
|
80 |
78 79
|
orbi12d |
|
81 |
73 80
|
bitr4id |
|
82 |
|
un00 |
|
83 |
82
|
bicomi |
|
84 |
|
df-3or |
|
85 |
81 83 84
|
3bitr4g |
|
86 |
70 85
|
bitrd |
|
87 |
67 86
|
pm2.61i |
|