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 |
1 2 3 4 5 6 7
|
ordtypelem8 |
|
9 |
1 2 3 4 5 6 7
|
ordtypelem4 |
|
10 |
9
|
frnd |
|
11 |
|
simprl |
|
12 |
6
|
adantr |
|
13 |
7
|
adantr |
|
14 |
9
|
ffund |
|
15 |
14
|
funfnd |
|
16 |
15
|
adantr |
|
17 |
1 2 3 4 5 12 13
|
ordtypelem8 |
|
18 |
|
isof1o |
|
19 |
|
f1of1 |
|
20 |
17 18 19
|
3syl |
|
21 |
|
simpl |
|
22 |
|
seex |
|
23 |
7 21 22
|
syl2an |
|
24 |
10
|
adantr |
|
25 |
|
rexnal |
|
26 |
1 2 3 4 5 6 7
|
ordtypelem7 |
|
27 |
26
|
ord |
|
28 |
27
|
rexlimdva |
|
29 |
25 28
|
syl5bir |
|
30 |
29
|
con1d |
|
31 |
30
|
impr |
|
32 |
|
breq1 |
|
33 |
32
|
ralrn |
|
34 |
16 33
|
syl |
|
35 |
31 34
|
mpbird |
|
36 |
|
ssrab |
|
37 |
24 35 36
|
sylanbrc |
|
38 |
23 37
|
ssexd |
|
39 |
|
f1dmex |
|
40 |
20 38 39
|
syl2anc |
|
41 |
16 40
|
fnexd |
|
42 |
1 2 3 4 5 12 13 41
|
ordtypelem9 |
|
43 |
|
isof1o |
|
44 |
|
f1ofo |
|
45 |
|
forn |
|
46 |
42 43 44 45
|
4syl |
|
47 |
11 46
|
eleqtrrd |
|
48 |
47
|
expr |
|
49 |
48
|
pm2.18d |
|
50 |
10 49
|
eqelssd |
|
51 |
|
isoeq5 |
|
52 |
50 51
|
syl |
|
53 |
8 52
|
mpbid |
|