Step |
Hyp |
Ref |
Expression |
1 |
|
fiuncmp.1 |
|
2 |
|
ssid |
|
3 |
|
simp2 |
|
4 |
|
sseq1 |
|
5 |
|
iuneq1 |
|
6 |
|
0iun |
|
7 |
5 6
|
eqtrdi |
|
8 |
7
|
oveq2d |
|
9 |
8
|
eleq1d |
|
10 |
4 9
|
imbi12d |
|
11 |
10
|
imbi2d |
|
12 |
|
sseq1 |
|
13 |
|
iuneq1 |
|
14 |
13
|
oveq2d |
|
15 |
14
|
eleq1d |
|
16 |
12 15
|
imbi12d |
|
17 |
16
|
imbi2d |
|
18 |
|
sseq1 |
|
19 |
|
iuneq1 |
|
20 |
19
|
oveq2d |
|
21 |
20
|
eleq1d |
|
22 |
18 21
|
imbi12d |
|
23 |
22
|
imbi2d |
|
24 |
|
sseq1 |
|
25 |
|
iuneq1 |
|
26 |
25
|
oveq2d |
|
27 |
26
|
eleq1d |
|
28 |
24 27
|
imbi12d |
|
29 |
28
|
imbi2d |
|
30 |
|
rest0 |
|
31 |
|
0cmp |
|
32 |
30 31
|
eqeltrdi |
|
33 |
32
|
3ad2ant1 |
|
34 |
33
|
a1d |
|
35 |
|
ssun1 |
|
36 |
|
id |
|
37 |
35 36
|
sstrid |
|
38 |
37
|
imim1i |
|
39 |
|
simpl1 |
|
40 |
|
iunxun |
|
41 |
|
simprr |
|
42 |
|
cmptop |
|
43 |
|
restrcl |
|
44 |
43
|
simprd |
|
45 |
41 42 44
|
3syl |
|
46 |
|
nfcv |
|
47 |
|
nfcsb1v |
|
48 |
|
csbeq1a |
|
49 |
46 47 48
|
cbviun |
|
50 |
|
vex |
|
51 |
|
csbeq1 |
|
52 |
50 51
|
iunxsn |
|
53 |
49 52
|
eqtri |
|
54 |
51
|
oveq2d |
|
55 |
54
|
eleq1d |
|
56 |
|
simpl3 |
|
57 |
|
nfv |
|
58 |
|
nfcv |
|
59 |
|
nfcv |
|
60 |
58 59 47
|
nfov |
|
61 |
60
|
nfel1 |
|
62 |
48
|
oveq2d |
|
63 |
62
|
eleq1d |
|
64 |
57 61 63
|
cbvralw |
|
65 |
56 64
|
sylib |
|
66 |
|
ssun2 |
|
67 |
|
simprl |
|
68 |
66 67
|
sstrid |
|
69 |
50
|
snss |
|
70 |
68 69
|
sylibr |
|
71 |
55 65 70
|
rspcdva |
|
72 |
|
cmptop |
|
73 |
|
restrcl |
|
74 |
73
|
simprd |
|
75 |
71 72 74
|
3syl |
|
76 |
53 75
|
eqeltrid |
|
77 |
|
unexg |
|
78 |
45 76 77
|
syl2anc |
|
79 |
40 78
|
eqeltrid |
|
80 |
|
resttop |
|
81 |
39 79 80
|
syl2anc |
|
82 |
|
eqid |
|
83 |
82
|
restin |
|
84 |
39 79 83
|
syl2anc |
|
85 |
84
|
unieqd |
|
86 |
|
inss2 |
|
87 |
86 1
|
sseqtrri |
|
88 |
1
|
restuni |
|
89 |
39 87 88
|
sylancl |
|
90 |
85 89
|
eqtr4d |
|
91 |
53
|
uneq2i |
|
92 |
40 91
|
eqtri |
|
93 |
92
|
ineq1i |
|
94 |
|
indir |
|
95 |
93 94
|
eqtri |
|
96 |
90 95
|
eqtrdi |
|
97 |
|
inss1 |
|
98 |
|
ssun1 |
|
99 |
98 40
|
sseqtrri |
|
100 |
97 99
|
sstri |
|
101 |
100
|
a1i |
|
102 |
|
restabs |
|
103 |
39 101 79 102
|
syl3anc |
|
104 |
82
|
restin |
|
105 |
39 45 104
|
syl2anc |
|
106 |
103 105
|
eqtr4d |
|
107 |
106 41
|
eqeltrd |
|
108 |
|
inss1 |
|
109 |
|
ssun2 |
|
110 |
109 40
|
sseqtrri |
|
111 |
53 110
|
eqsstrri |
|
112 |
108 111
|
sstri |
|
113 |
112
|
a1i |
|
114 |
|
restabs |
|
115 |
39 113 79 114
|
syl3anc |
|
116 |
82
|
restin |
|
117 |
39 75 116
|
syl2anc |
|
118 |
115 117
|
eqtr4d |
|
119 |
118 71
|
eqeltrd |
|
120 |
|
eqid |
|
121 |
120
|
uncmp |
|
122 |
81 96 107 119 121
|
syl22anc |
|
123 |
122
|
exp32 |
|
124 |
123
|
a2d |
|
125 |
38 124
|
syl5 |
|
126 |
125
|
a2i |
|
127 |
126
|
a1i |
|
128 |
11 17 23 29 34 127
|
findcard2 |
|
129 |
3 128
|
mpcom |
|
130 |
2 129
|
mpi |
|