Step |
Hyp |
Ref |
Expression |
1 |
|
ackbij.f |
|
2 |
1
|
ackbij1lem8 |
|
3 |
|
pweq |
|
4 |
3
|
fveq2d |
|
5 |
|
fveq2 |
|
6 |
|
suceq |
|
7 |
5 6
|
syl |
|
8 |
4 7
|
eqeq12d |
|
9 |
|
pweq |
|
10 |
9
|
fveq2d |
|
11 |
|
fveq2 |
|
12 |
|
suceq |
|
13 |
11 12
|
syl |
|
14 |
10 13
|
eqeq12d |
|
15 |
|
pweq |
|
16 |
15
|
fveq2d |
|
17 |
|
fveq2 |
|
18 |
|
suceq |
|
19 |
17 18
|
syl |
|
20 |
16 19
|
eqeq12d |
|
21 |
|
pweq |
|
22 |
21
|
fveq2d |
|
23 |
|
fveq2 |
|
24 |
|
suceq |
|
25 |
23 24
|
syl |
|
26 |
22 25
|
eqeq12d |
|
27 |
|
df-1o |
|
28 |
|
pw0 |
|
29 |
28
|
fveq2i |
|
30 |
|
0ex |
|
31 |
|
cardsn |
|
32 |
30 31
|
ax-mp |
|
33 |
29 32
|
eqtri |
|
34 |
1
|
ackbij1lem13 |
|
35 |
|
suceq |
|
36 |
34 35
|
ax-mp |
|
37 |
27 33 36
|
3eqtr4i |
|
38 |
|
oveq2 |
|
39 |
38
|
adantl |
|
40 |
|
ackbij1lem5 |
|
41 |
40
|
adantr |
|
42 |
|
df-suc |
|
43 |
42
|
equncomi |
|
44 |
43
|
fveq2i |
|
45 |
|
ackbij1lem4 |
|
46 |
45
|
adantr |
|
47 |
|
ackbij1lem3 |
|
48 |
47
|
adantr |
|
49 |
|
incom |
|
50 |
|
nnord |
|
51 |
|
orddisj |
|
52 |
50 51
|
syl |
|
53 |
49 52
|
syl5eq |
|
54 |
53
|
adantr |
|
55 |
1
|
ackbij1lem9 |
|
56 |
46 48 54 55
|
syl3anc |
|
57 |
1
|
ackbij1lem8 |
|
58 |
57
|
adantr |
|
59 |
58
|
oveq1d |
|
60 |
56 59
|
eqtrd |
|
61 |
44 60
|
syl5eq |
|
62 |
|
suceq |
|
63 |
61 62
|
syl |
|
64 |
|
nnfi |
|
65 |
|
pwfi |
|
66 |
64 65
|
sylib |
|
67 |
66
|
adantr |
|
68 |
|
ficardom |
|
69 |
67 68
|
syl |
|
70 |
1
|
ackbij1lem10 |
|
71 |
70
|
ffvelrni |
|
72 |
48 71
|
syl |
|
73 |
|
nnasuc |
|
74 |
69 72 73
|
syl2anc |
|
75 |
63 74
|
eqtr4d |
|
76 |
39 41 75
|
3eqtr4d |
|
77 |
76
|
ex |
|
78 |
8 14 20 26 37 77
|
finds |
|
79 |
2 78
|
eqtrd |
|