Step |
Hyp |
Ref |
Expression |
1 |
|
ackbij.f |
|
2 |
|
difss |
|
3 |
1
|
ackbij1lem11 |
|
4 |
2 3
|
mpan2 |
|
5 |
|
difss |
|
6 |
|
omsson |
|
7 |
5 6
|
sstri |
|
8 |
|
ominf |
|
9 |
|
elinel2 |
|
10 |
|
difinf |
|
11 |
8 9 10
|
sylancr |
|
12 |
|
0fin |
|
13 |
|
eleq1 |
|
14 |
12 13
|
mpbiri |
|
15 |
14
|
necon3bi |
|
16 |
11 15
|
syl |
|
17 |
|
onint |
|
18 |
7 16 17
|
sylancr |
|
19 |
18
|
eldifad |
|
20 |
|
ackbij1lem4 |
|
21 |
19 20
|
syl |
|
22 |
|
ackbij1lem6 |
|
23 |
4 21 22
|
syl2anc |
|
24 |
18
|
eldifbd |
|
25 |
|
disjsn |
|
26 |
24 25
|
sylibr |
|
27 |
|
ssdisj |
|
28 |
2 26 27
|
sylancr |
|
29 |
1
|
ackbij1lem9 |
|
30 |
4 21 28 29
|
syl3anc |
|
31 |
1
|
ackbij1lem14 |
|
32 |
19 31
|
syl |
|
33 |
32
|
oveq2d |
|
34 |
1
|
ackbij1lem10 |
|
35 |
34
|
ffvelrni |
|
36 |
4 35
|
syl |
|
37 |
|
ackbij1lem3 |
|
38 |
19 37
|
syl |
|
39 |
34
|
ffvelrni |
|
40 |
38 39
|
syl |
|
41 |
|
nnasuc |
|
42 |
36 40 41
|
syl2anc |
|
43 |
|
incom |
|
44 |
|
disjdif |
|
45 |
43 44
|
eqtri |
|
46 |
45
|
a1i |
|
47 |
1
|
ackbij1lem9 |
|
48 |
4 38 46 47
|
syl3anc |
|
49 |
|
uncom |
|
50 |
|
onnmin |
|
51 |
7 50
|
mpan |
|
52 |
51
|
con2i |
|
53 |
52
|
adantl |
|
54 |
|
ordom |
|
55 |
|
ordelss |
|
56 |
54 19 55
|
sylancr |
|
57 |
56
|
sselda |
|
58 |
|
eldif |
|
59 |
58
|
simplbi2 |
|
60 |
59
|
orrd |
|
61 |
60
|
orcomd |
|
62 |
57 61
|
syl |
|
63 |
|
orel1 |
|
64 |
53 62 63
|
sylc |
|
65 |
64
|
ex |
|
66 |
65
|
ssrdv |
|
67 |
|
undif |
|
68 |
66 67
|
sylib |
|
69 |
49 68
|
syl5eq |
|
70 |
69
|
fveq2d |
|
71 |
48 70
|
eqtr3d |
|
72 |
|
suceq |
|
73 |
71 72
|
syl |
|
74 |
42 73
|
eqtrd |
|
75 |
30 33 74
|
3eqtrd |
|
76 |
|
fveqeq2 |
|
77 |
76
|
rspcev |
|
78 |
23 75 77
|
syl2anc |
|