Step |
Hyp |
Ref |
Expression |
1 |
|
eldif |
|
2 |
|
omelon |
|
3 |
|
cardon |
|
4 |
|
eleq1 |
|
5 |
3 4
|
mpbii |
|
6 |
|
ontri1 |
|
7 |
2 5 6
|
sylancr |
|
8 |
7
|
pm5.32i |
|
9 |
|
iscard4 |
|
10 |
9
|
anbi1i |
|
11 |
8 10
|
bitr2i |
|
12 |
|
ancom |
|
13 |
1 11 12
|
3bitri |
|
14 |
13
|
biimpi |
|
15 |
|
cardalephex |
|
16 |
15
|
biimpa |
|
17 |
|
eqimss |
|
18 |
17
|
a1i |
|
19 |
18
|
reximdv |
|
20 |
16 19
|
mpd |
|
21 |
|
onintrab2 |
|
22 |
20 21
|
sylib |
|
23 |
|
simpr |
|
24 |
|
onsuc |
|
25 |
23 24
|
syl |
|
26 |
|
eloni |
|
27 |
23 26
|
syl |
|
28 |
|
0elsuc |
|
29 |
27 28
|
syl |
|
30 |
|
cardaleph |
|
31 |
30
|
adantr |
|
32 |
|
sssucid |
|
33 |
|
alephord3 |
|
34 |
23 24 33
|
syl2anc2 |
|
35 |
32 34
|
mpbii |
|
36 |
31 35
|
eqsstrd |
|
37 |
|
alephreg |
|
38 |
37
|
a1i |
|
39 |
29 36 38
|
3jca |
|
40 |
25 39
|
jca |
|
41 |
14 22 40
|
syl2anc2 |
|
42 |
14 16
|
syl |
|
43 |
17
|
a1i |
|
44 |
43
|
reximdv |
|
45 |
42 44
|
mpd |
|
46 |
45 21
|
sylib |
|
47 |
46 24
|
syl |
|
48 |
|
sbcan |
|
49 |
|
sbcel1v |
|
50 |
49
|
a1i |
|
51 |
|
sbc3an |
|
52 |
|
sbcel2gv |
|
53 |
|
sbcssg |
|
54 |
|
csbconstg |
|
55 |
|
csbfv2g |
|
56 |
|
csbvarg |
|
57 |
56
|
fveq2d |
|
58 |
55 57
|
eqtrd |
|
59 |
54 58
|
sseq12d |
|
60 |
53 59
|
bitrd |
|
61 |
|
sbceqg |
|
62 |
|
csbfv2g |
|
63 |
58
|
fveq2d |
|
64 |
62 63
|
eqtrd |
|
65 |
64 58
|
eqeq12d |
|
66 |
61 65
|
bitrd |
|
67 |
52 60 66
|
3anbi123d |
|
68 |
51 67
|
bitrid |
|
69 |
50 68
|
anbi12d |
|
70 |
48 69
|
bitrid |
|
71 |
47 70
|
syl |
|
72 |
41 71
|
mpbird |
|
73 |
72
|
spesbcd |
|
74 |
|
onintrab2 |
|
75 |
|
df-rex |
|
76 |
|
risset |
|
77 |
74 75 76
|
3bitr3i |
|
78 |
73 77
|
sylib |
|