Step |
Hyp |
Ref |
Expression |
1 |
|
ordttopon.3 |
|
2 |
|
eqid |
|
3 |
|
eqid |
|
4 |
1 2 3
|
ordtuni |
|
5 |
4
|
adantr |
|
6 |
|
dmexg |
|
7 |
1 6
|
eqeltrid |
|
8 |
7
|
adantr |
|
9 |
5 8
|
eqeltrrd |
|
10 |
|
uniexb |
|
11 |
9 10
|
sylibr |
|
12 |
|
ssfii |
|
13 |
11 12
|
syl |
|
14 |
|
fibas |
|
15 |
|
bastg |
|
16 |
14 15
|
ax-mp |
|
17 |
13 16
|
sstrdi |
|
18 |
1 2 3
|
ordtval |
|
19 |
18
|
adantr |
|
20 |
17 19
|
sseqtrrd |
|
21 |
|
ssun2 |
|
22 |
|
ssun2 |
|
23 |
|
simpr |
|
24 |
|
eqidd |
|
25 |
|
breq1 |
|
26 |
25
|
notbid |
|
27 |
26
|
rabbidv |
|
28 |
27
|
rspceeqv |
|
29 |
23 24 28
|
syl2anc |
|
30 |
|
rabexg |
|
31 |
|
eqid |
|
32 |
31
|
elrnmpt |
|
33 |
8 30 32
|
3syl |
|
34 |
29 33
|
mpbird |
|
35 |
22 34
|
sseldi |
|
36 |
21 35
|
sseldi |
|
37 |
20 36
|
sseldd |
|