Step |
Hyp |
Ref |
Expression |
1 |
|
cnfcom3c |
|
2 |
|
df-2o |
|
3 |
2
|
oveq2i |
|
4 |
|
omelon |
|
5 |
|
1on |
|
6 |
|
oesuc |
|
7 |
4 5 6
|
mp2an |
|
8 |
|
oe1 |
|
9 |
4 8
|
ax-mp |
|
10 |
9
|
oveq1i |
|
11 |
3 7 10
|
3eqtri |
|
12 |
|
omxpen |
|
13 |
4 4 12
|
mp2an |
|
14 |
11 13
|
eqbrtri |
|
15 |
|
xpomen |
|
16 |
14 15
|
entri |
|
17 |
16
|
a1i |
|
18 |
|
bren |
|
19 |
17 18
|
sylib |
|
20 |
|
exdistrv |
|
21 |
|
simpl |
|
22 |
|
simprl |
|
23 |
|
sseq2 |
|
24 |
|
oveq2 |
|
25 |
24
|
f1oeq3d |
|
26 |
25
|
cbvrexvw |
|
27 |
|
fveq2 |
|
28 |
|
f1oeq1 |
|
29 |
27 28
|
syl |
|
30 |
|
f1oeq2 |
|
31 |
29 30
|
bitrd |
|
32 |
31
|
rexbidv |
|
33 |
26 32
|
syl5bb |
|
34 |
23 33
|
imbi12d |
|
35 |
34
|
cbvralvw |
|
36 |
22 35
|
sylib |
|
37 |
|
oveq2 |
|
38 |
37
|
cbvmptv |
|
39 |
38
|
cnveqi |
|
40 |
39
|
fveq1i |
|
41 |
|
2on |
|
42 |
|
peano1 |
|
43 |
|
oen0 |
|
44 |
42 43
|
mpan2 |
|
45 |
4 41 44
|
mp2an |
|
46 |
|
eqid |
|
47 |
46
|
fveqf1o |
|
48 |
45 42 47
|
mp3an23 |
|
49 |
48
|
ad2antll |
|
50 |
49
|
simpld |
|
51 |
49
|
simprd |
|
52 |
21 36 40 50 51
|
infxpenc2lem3 |
|
53 |
52
|
ex |
|
54 |
53
|
exlimdvv |
|
55 |
20 54
|
syl5bir |
|
56 |
1 19 55
|
mp2and |
|