Step |
Hyp |
Ref |
Expression |
1 |
|
funres |
|
2 |
|
funfn |
|
3 |
|
funfn |
|
4 |
1 2 3
|
3imtr3i |
|
5 |
|
resss |
|
6 |
5
|
rnssi |
|
7 |
|
sstr |
|
8 |
6 7
|
mpan |
|
9 |
4 8
|
anim12i |
|
10 |
|
df-f |
|
11 |
|
df-f |
|
12 |
9 10 11
|
3imtr4i |
|
13 |
12
|
a1i |
|
14 |
|
ordelord |
|
15 |
14
|
expcom |
|
16 |
|
ordin |
|
17 |
16
|
ex |
|
18 |
15 17
|
syli |
|
19 |
|
dmres |
|
20 |
|
ordeq |
|
21 |
19 20
|
ax-mp |
|
22 |
18 21
|
syl6ibr |
|
23 |
|
dmss |
|
24 |
5 23
|
ax-mp |
|
25 |
|
ssralv |
|
26 |
24 25
|
ax-mp |
|
27 |
|
ssralv |
|
28 |
24 27
|
ax-mp |
|
29 |
28
|
ralimi |
|
30 |
26 29
|
syl |
|
31 |
|
inss1 |
|
32 |
19 31
|
eqsstri |
|
33 |
|
simpl |
|
34 |
32 33
|
sselid |
|
35 |
34
|
fvresd |
|
36 |
|
simpr |
|
37 |
32 36
|
sselid |
|
38 |
37
|
fvresd |
|
39 |
35 38
|
eleq12d |
|
40 |
39
|
imbi2d |
|
41 |
40
|
ralbidva |
|
42 |
41
|
ralbiia |
|
43 |
30 42
|
sylibr |
|
44 |
43
|
a1i |
|
45 |
13 22 44
|
3anim123d |
|
46 |
|
df-smo |
|
47 |
|
df-smo |
|
48 |
45 46 47
|
3imtr4g |
|
49 |
48
|
impcom |
|