Step |
Hyp |
Ref |
Expression |
1 |
|
oesuclem.1 |
|
2 |
|
oesuclem.2 |
|
3 |
|
oveq1 |
|
4 |
|
limord |
|
5 |
1 4
|
ax-mp |
|
6 |
|
ordelord |
|
7 |
5 6
|
mpan |
|
8 |
|
0elsuc |
|
9 |
7 8
|
syl |
|
10 |
|
limsuc |
|
11 |
1 10
|
ax-mp |
|
12 |
|
ordelon |
|
13 |
5 12
|
mpan |
|
14 |
|
oe0m1 |
|
15 |
13 14
|
syl |
|
16 |
11 15
|
sylbi |
|
17 |
9 16
|
mpbid |
|
18 |
3 17
|
sylan9eqr |
|
19 |
|
oveq1 |
|
20 |
|
id |
|
21 |
19 20
|
oveq12d |
|
22 |
|
ordelon |
|
23 |
5 22
|
mpan |
|
24 |
|
oveq2 |
|
25 |
|
oe0m0 |
|
26 |
|
1on |
|
27 |
25 26
|
eqeltri |
|
28 |
24 27
|
eqeltrdi |
|
29 |
28
|
adantl |
|
30 |
|
oe0m1 |
|
31 |
23 30
|
syl |
|
32 |
31
|
biimpa |
|
33 |
|
0elon |
|
34 |
32 33
|
eqeltrdi |
|
35 |
34
|
adantll |
|
36 |
29 35
|
oe0lem |
|
37 |
23 36
|
mpancom |
|
38 |
|
om0 |
|
39 |
37 38
|
syl |
|
40 |
21 39
|
sylan9eqr |
|
41 |
18 40
|
eqtr4d |
|
42 |
2
|
ad2antlr |
|
43 |
11 13
|
sylbi |
|
44 |
|
oevn0 |
|
45 |
43 44
|
sylanl2 |
|
46 |
|
ovex |
|
47 |
|
oveq1 |
|
48 |
|
eqid |
|
49 |
|
ovex |
|
50 |
47 48 49
|
fvmpt |
|
51 |
46 50
|
ax-mp |
|
52 |
|
oevn0 |
|
53 |
23 52
|
sylanl2 |
|
54 |
53
|
fveq2d |
|
55 |
51 54
|
syl5eqr |
|
56 |
42 45 55
|
3eqtr4d |
|
57 |
41 56
|
oe0lem |
|