Step |
Hyp |
Ref |
Expression |
1 |
|
finxpsuclem.1 |
|
2 |
|
peano2 |
|
3 |
2
|
adantr |
|
4 |
|
1on |
|
5 |
4
|
onordi |
|
6 |
|
nnord |
|
7 |
|
ordsseleq |
|
8 |
5 6 7
|
sylancr |
|
9 |
8
|
biimpa |
|
10 |
|
elelsuc |
|
11 |
10
|
a1i |
|
12 |
|
sucidg |
|
13 |
|
eleq1 |
|
14 |
12 13
|
syl5ibrcom |
|
15 |
11 14
|
jaod |
|
16 |
15
|
adantr |
|
17 |
9 16
|
mpd |
|
18 |
1
|
finxpreclem6 |
|
19 |
3 17 18
|
syl2anc |
|
20 |
19
|
sselda |
|
21 |
2
|
ad2antrr |
|
22 |
|
df-2o |
|
23 |
|
ordsucsssuc |
|
24 |
5 6 23
|
sylancr |
|
25 |
24
|
biimpa |
|
26 |
22 25
|
eqsstrid |
|
27 |
26
|
adantr |
|
28 |
|
simpr |
|
29 |
1
|
finxpreclem4 |
|
30 |
21 27 28 29
|
syl21anc |
|
31 |
|
ordunisuc |
|
32 |
6 31
|
syl |
|
33 |
|
opeq1 |
|
34 |
|
rdgeq2 |
|
35 |
33 34
|
syl |
|
36 |
32 35
|
syl |
|
37 |
36 32
|
fveq12d |
|
38 |
37
|
ad2antrr |
|
39 |
30 38
|
eqtrd |
|
40 |
39
|
eqeq2d |
|
41 |
1
|
dffinxpf |
|
42 |
41
|
abeq2i |
|
43 |
2
|
biantrurd |
|
44 |
42 43
|
bitr4id |
|
45 |
44
|
ad2antrr |
|
46 |
|
fvex |
|
47 |
|
opeq2 |
|
48 |
|
rdgeq2 |
|
49 |
47 48
|
syl |
|
50 |
49
|
fveq1d |
|
51 |
50
|
eqeq2d |
|
52 |
51
|
anbi2d |
|
53 |
1
|
dffinxpf |
|
54 |
46 52 53
|
elab2 |
|
55 |
54
|
baib |
|
56 |
55
|
ad2antrr |
|
57 |
40 45 56
|
3bitr4d |
|
58 |
57
|
biimpd |
|
59 |
58
|
impancom |
|
60 |
20 59
|
mpd |
|
61 |
60
|
ex |
|
62 |
20
|
ex |
|
63 |
61 62
|
jcad |
|
64 |
57
|
exbiri |
|
65 |
64
|
impd |
|
66 |
65
|
ancomsd |
|
67 |
63 66
|
impbid |
|
68 |
|
elxp8 |
|
69 |
67 68
|
bitr4di |
|
70 |
69
|
eqrdv |
|