Step |
Hyp |
Ref |
Expression |
1 |
|
dfsmo2 |
|
2 |
1
|
simp1bi |
|
3 |
2
|
ffund |
|
4 |
|
funres |
|
5 |
4
|
funfnd |
|
6 |
3 5
|
syl |
|
7 |
|
df-ima |
|
8 |
|
imassrn |
|
9 |
7 8
|
eqsstrri |
|
10 |
2
|
frnd |
|
11 |
9 10
|
sstrid |
|
12 |
|
df-f |
|
13 |
6 11 12
|
sylanbrc |
|
14 |
13
|
adantr |
|
15 |
|
smodm |
|
16 |
|
ordin |
|
17 |
|
dmres |
|
18 |
|
ordeq |
|
19 |
17 18
|
ax-mp |
|
20 |
16 19
|
sylibr |
|
21 |
20
|
ancoms |
|
22 |
15 21
|
sylan |
|
23 |
|
resss |
|
24 |
|
dmss |
|
25 |
23 24
|
ax-mp |
|
26 |
1
|
simp3bi |
|
27 |
|
ssralv |
|
28 |
25 26 27
|
mpsyl |
|
29 |
28
|
adantr |
|
30 |
|
ordtr1 |
|
31 |
22 30
|
syl |
|
32 |
|
inss1 |
|
33 |
17 32
|
eqsstri |
|
34 |
33
|
sseli |
|
35 |
31 34
|
syl6 |
|
36 |
35
|
expcomd |
|
37 |
36
|
imp31 |
|
38 |
37
|
fvresd |
|
39 |
33
|
sseli |
|
40 |
39
|
fvresd |
|
41 |
40
|
ad2antlr |
|
42 |
38 41
|
eleq12d |
|
43 |
42
|
ralbidva |
|
44 |
43
|
ralbidva |
|
45 |
29 44
|
mpbird |
|
46 |
|
dfsmo2 |
|
47 |
14 22 45 46
|
syl3anbrc |
|