Step |
Hyp |
Ref |
Expression |
1 |
|
disjunsn.s |
|
2 |
|
disjors |
|
3 |
|
eqeq1 |
|
4 |
|
csbeq1 |
|
5 |
4
|
ineq1d |
|
6 |
5
|
eqeq1d |
|
7 |
3 6
|
orbi12d |
|
8 |
7
|
ralbidv |
|
9 |
8
|
ralunsn |
|
10 |
2 9
|
syl5bb |
|
11 |
|
eqeq2 |
|
12 |
|
csbeq1 |
|
13 |
12
|
ineq2d |
|
14 |
13
|
eqeq1d |
|
15 |
11 14
|
orbi12d |
|
16 |
15
|
ralunsn |
|
17 |
16
|
ralbidv |
|
18 |
|
eqeq2 |
|
19 |
12
|
ineq2d |
|
20 |
19
|
eqeq1d |
|
21 |
18 20
|
orbi12d |
|
22 |
21
|
ralunsn |
|
23 |
|
eqid |
|
24 |
23
|
orci |
|
25 |
24
|
biantru |
|
26 |
22 25
|
bitr4di |
|
27 |
17 26
|
anbi12d |
|
28 |
10 27
|
bitrd |
|
29 |
|
r19.26 |
|
30 |
|
disjors |
|
31 |
30
|
anbi1i |
|
32 |
29 31
|
bitr4i |
|
33 |
32
|
anbi1i |
|
34 |
28 33
|
syl6bb |
|
35 |
34
|
adantr |
|
36 |
|
orcom |
|
37 |
36
|
ralbii |
|
38 |
|
r19.30 |
|
39 |
|
risset |
|
40 |
|
biorf |
|
41 |
39 40
|
sylnbi |
|
42 |
41
|
adantl |
|
43 |
|
orcom |
|
44 |
42 43
|
syl6bb |
|
45 |
38 44
|
syl5ibr |
|
46 |
37 45
|
syl5bir |
|
47 |
|
olc |
|
48 |
47
|
ralimi |
|
49 |
46 48
|
impbid1 |
|
50 |
|
nfv |
|
51 |
|
nfcsb1v |
|
52 |
|
nfcv |
|
53 |
51 52
|
nfin |
|
54 |
53
|
nfeq1 |
|
55 |
|
csbeq1a |
|
56 |
55
|
ineq1d |
|
57 |
56
|
eqeq1d |
|
58 |
50 54 57
|
cbvralw |
|
59 |
58
|
a1i |
|
60 |
|
ss0b |
|
61 |
|
iunss |
|
62 |
|
iunin1 |
|
63 |
62
|
eqeq1i |
|
64 |
60 61 63
|
3bitr3ri |
|
65 |
|
ss0b |
|
66 |
65
|
ralbii |
|
67 |
64 66
|
bitri |
|
68 |
67
|
a1i |
|
69 |
|
nfcvd |
|
70 |
69 1
|
csbiegf |
|
71 |
70
|
ineq2d |
|
72 |
71
|
eqeq1d |
|
73 |
72
|
ralbidv |
|
74 |
59 68 73
|
3bitr4d |
|
75 |
74
|
adantr |
|
76 |
49 75
|
bitr4d |
|
77 |
76
|
anbi2d |
|
78 |
|
orcom |
|
79 |
78
|
ralbii |
|
80 |
|
r19.30 |
|
81 |
|
clel5 |
|
82 |
|
biorf |
|
83 |
81 82
|
sylnbi |
|
84 |
83
|
adantl |
|
85 |
|
orcom |
|
86 |
84 85
|
syl6bb |
|
87 |
80 86
|
syl5ibr |
|
88 |
79 87
|
syl5bir |
|
89 |
|
olc |
|
90 |
89
|
ralimi |
|
91 |
88 90
|
impbid1 |
|
92 |
|
nfv |
|
93 |
|
nfcsb1v |
|
94 |
93 52
|
nfin |
|
95 |
94
|
nfeq1 |
|
96 |
|
csbeq1a |
|
97 |
96
|
ineq1d |
|
98 |
97
|
eqeq1d |
|
99 |
92 95 98
|
cbvralw |
|
100 |
99
|
a1i |
|
101 |
|
incom |
|
102 |
101
|
eqeq1i |
|
103 |
102
|
ralbii |
|
104 |
100 103
|
syl6bb |
|
105 |
70
|
ineq1d |
|
106 |
105
|
eqeq1d |
|
107 |
106
|
ralbidv |
|
108 |
104 68 107
|
3bitr4d |
|
109 |
108
|
adantr |
|
110 |
91 109
|
bitr4d |
|
111 |
77 110
|
anbi12d |
|
112 |
|
anass |
|
113 |
|
anidm |
|
114 |
113
|
anbi2i |
|
115 |
112 114
|
bitri |
|
116 |
111 115
|
syl6bb |
|
117 |
35 116
|
bitrd |
|