Step |
Hyp |
Ref |
Expression |
1 |
|
orduni |
|
2 |
|
unizlim |
|
3 |
|
uni0b |
|
4 |
3
|
orbi1i |
|
5 |
2 4
|
syl6bb |
|
6 |
5
|
biimpd |
|
7 |
1 6
|
syl |
|
8 |
|
sssn |
|
9 |
|
0ntop |
|
10 |
|
cmptop |
|
11 |
9 10
|
mto |
|
12 |
|
eleq1 |
|
13 |
11 12
|
mtbiri |
|
14 |
13
|
pm2.21d |
|
15 |
|
id |
|
16 |
|
df1o2 |
|
17 |
15 16
|
eqtr4di |
|
18 |
17
|
a1d |
|
19 |
14 18
|
jaoi |
|
20 |
8 19
|
sylbi |
|
21 |
20
|
a1i |
|
22 |
|
ordtop |
|
23 |
22
|
biimpd |
|
24 |
23
|
necon2bd |
|
25 |
|
cmptop |
|
26 |
25
|
con3i |
|
27 |
24 26
|
syl6 |
|
28 |
27
|
a1dd |
|
29 |
|
limsucncmp |
|
30 |
|
eleq1 |
|
31 |
30
|
notbid |
|
32 |
29 31
|
syl5ibr |
|
33 |
32
|
a1i |
|
34 |
|
orduniorsuc |
|
35 |
28 33 34
|
mpjaod |
|
36 |
|
pm2.21 |
|
37 |
35 36
|
syl6 |
|
38 |
21 37
|
jaod |
|
39 |
38
|
com23 |
|
40 |
7 39
|
syl5d |
|
41 |
|
ordeleqon |
|
42 |
|
unon |
|
43 |
42
|
eqcomi |
|
44 |
43
|
unieqi |
|
45 |
|
unieq |
|
46 |
45
|
unieqd |
|
47 |
44 45 46
|
3eqtr4a |
|
48 |
47
|
orim2i |
|
49 |
41 48
|
sylbi |
|
50 |
49
|
orcomd |
|
51 |
50
|
ord |
|
52 |
|
unieq |
|
53 |
52
|
con3i |
|
54 |
34
|
ord |
|
55 |
53 54
|
syl5 |
|
56 |
|
orduniorsuc |
|
57 |
1 56
|
syl |
|
58 |
57
|
ord |
|
59 |
|
suceq |
|
60 |
58 59
|
syl6 |
|
61 |
|
eqtr |
|
62 |
61
|
ex |
|
63 |
55 60 62
|
syl6c |
|
64 |
|
onuni |
|
65 |
|
onuni |
|
66 |
|
onsucsuccmp |
|
67 |
|
eleq1a |
|
68 |
64 65 66 67
|
4syl |
|
69 |
51 63 68
|
syl6c |
|
70 |
|
id |
|
71 |
70 16
|
eqtrdi |
|
72 |
|
0cmp |
|
73 |
71 72
|
eqeltrdi |
|
74 |
73
|
a1i |
|
75 |
69 74
|
jad |
|
76 |
40 75
|
impbid |
|