Step |
Hyp |
Ref |
Expression |
1 |
|
bren |
|
2 |
|
elpwi |
|
3 |
|
imauni |
|
4 |
|
vex |
|
5 |
4
|
imaex |
|
6 |
5
|
dfiun2 |
|
7 |
3 6
|
eqtri |
|
8 |
|
imaeq2 |
|
9 |
8
|
eleq1d |
|
10 |
9
|
rexrab |
|
11 |
|
eleq1 |
|
12 |
11
|
biimparc |
|
13 |
12
|
rexlimivw |
|
14 |
|
cnvimass |
|
15 |
|
f1odm |
|
16 |
15
|
ad3antrrr |
|
17 |
14 16
|
sseqtrid |
|
18 |
4
|
cnvex |
|
19 |
18
|
imaex |
|
20 |
19
|
elpw |
|
21 |
17 20
|
sylibr |
|
22 |
|
f1ofo |
|
23 |
22
|
ad3antrrr |
|
24 |
|
simprl |
|
25 |
24
|
sselda |
|
26 |
25
|
elpwid |
|
27 |
|
foimacnv |
|
28 |
23 26 27
|
syl2anc |
|
29 |
28
|
eqcomd |
|
30 |
|
simpr |
|
31 |
29 30
|
eqeltrrd |
|
32 |
|
imaeq2 |
|
33 |
32
|
eleq1d |
|
34 |
32
|
eqeq2d |
|
35 |
33 34
|
anbi12d |
|
36 |
35
|
rspcev |
|
37 |
21 31 29 36
|
syl12anc |
|
38 |
37
|
ex |
|
39 |
13 38
|
impbid2 |
|
40 |
10 39
|
syl5bb |
|
41 |
40
|
abbi1dv |
|
42 |
41
|
unieqd |
|
43 |
7 42
|
syl5eq |
|
44 |
|
simplr |
|
45 |
|
ssrab2 |
|
46 |
45
|
a1i |
|
47 |
|
simprrl |
|
48 |
|
n0 |
|
49 |
47 48
|
sylib |
|
50 |
|
imaeq2 |
|
51 |
50
|
eleq1d |
|
52 |
51
|
rspcev |
|
53 |
21 31 52
|
syl2anc |
|
54 |
49 53
|
exlimddv |
|
55 |
|
rabn0 |
|
56 |
54 55
|
sylibr |
|
57 |
9
|
elrab |
|
58 |
|
imaeq2 |
|
59 |
58
|
eleq1d |
|
60 |
59
|
elrab |
|
61 |
57 60
|
anbi12i |
|
62 |
|
simprrr |
|
63 |
62
|
adantr |
|
64 |
|
simprlr |
|
65 |
|
simprrr |
|
66 |
|
sorpssi |
|
67 |
63 64 65 66
|
syl12anc |
|
68 |
|
f1of1 |
|
69 |
68
|
ad3antrrr |
|
70 |
|
simprll |
|
71 |
70
|
elpwid |
|
72 |
|
simprrl |
|
73 |
72
|
elpwid |
|
74 |
|
f1imass |
|
75 |
69 71 73 74
|
syl12anc |
|
76 |
|
f1imass |
|
77 |
69 73 71 76
|
syl12anc |
|
78 |
75 77
|
orbi12d |
|
79 |
67 78
|
mpbid |
|
80 |
61 79
|
sylan2b |
|
81 |
80
|
ralrimivva |
|
82 |
|
sorpss |
|
83 |
81 82
|
sylibr |
|
84 |
|
fin2i |
|
85 |
44 46 56 83 84
|
syl22anc |
|
86 |
|
imaeq2 |
|
87 |
86
|
eleq1d |
|
88 |
9
|
cbvrabv |
|
89 |
87 88
|
elrab2 |
|
90 |
89
|
simprbi |
|
91 |
85 90
|
syl |
|
92 |
43 91
|
eqeltrrd |
|
93 |
92
|
expr |
|
94 |
2 93
|
sylan2 |
|
95 |
94
|
ralrimiva |
|
96 |
95
|
ex |
|
97 |
96
|
exlimiv |
|
98 |
1 97
|
sylbi |
|
99 |
|
relen |
|
100 |
99
|
brrelex2i |
|
101 |
|
isfin2 |
|
102 |
100 101
|
syl |
|
103 |
98 102
|
sylibrd |
|