Step |
Hyp |
Ref |
Expression |
1 |
|
ordtypelem.1 |
|
2 |
|
ordtypelem.2 |
|
3 |
|
ordtypelem.3 |
|
4 |
|
ordtypelem.5 |
|
5 |
|
ordtypelem.6 |
|
6 |
|
ordtypelem.7 |
|
7 |
|
ordtypelem.8 |
|
8 |
|
fveq2 |
|
9 |
8
|
breq1d |
|
10 |
|
ssrab2 |
|
11 |
|
simpr |
|
12 |
1 2 3 4 5 6 7
|
ordtypelem4 |
|
13 |
12
|
fdmd |
|
14 |
13
|
adantr |
|
15 |
11 14
|
eleqtrd |
|
16 |
1 2 3 4 5 6 7
|
ordtypelem3 |
|
17 |
15 16
|
syldan |
|
18 |
10 17
|
sselid |
|
19 |
|
breq2 |
|
20 |
19
|
ralbidv |
|
21 |
20
|
elrab |
|
22 |
21
|
simprbi |
|
23 |
18 22
|
syl |
|
24 |
1
|
tfr1a |
|
25 |
24
|
simpli |
|
26 |
|
funfn |
|
27 |
25 26
|
mpbi |
|
28 |
24
|
simpri |
|
29 |
|
limord |
|
30 |
28 29
|
ax-mp |
|
31 |
|
inss2 |
|
32 |
13 31
|
eqsstrdi |
|
33 |
32
|
sselda |
|
34 |
|
ordelss |
|
35 |
30 33 34
|
sylancr |
|
36 |
|
breq1 |
|
37 |
36
|
ralima |
|
38 |
27 35 37
|
sylancr |
|
39 |
23 38
|
mpbid |
|
40 |
39
|
adantrr |
|
41 |
|
simprr |
|
42 |
9 40 41
|
rspcdva |
|
43 |
1 2 3 4 5 6 7
|
ordtypelem1 |
|
44 |
43
|
adantr |
|
45 |
44
|
fveq1d |
|
46 |
1 2 3 4 5 6 7
|
ordtypelem2 |
|
47 |
|
inss1 |
|
48 |
13 47
|
eqsstrdi |
|
49 |
48
|
sselda |
|
50 |
49
|
adantrr |
|
51 |
|
ordelss |
|
52 |
46 50 51
|
syl2an2r |
|
53 |
52 41
|
sseldd |
|
54 |
53
|
fvresd |
|
55 |
45 54
|
eqtrd |
|
56 |
44
|
fveq1d |
|
57 |
50
|
fvresd |
|
58 |
56 57
|
eqtrd |
|
59 |
42 55 58
|
3brtr4d |
|
60 |
59
|
expr |
|