Step |
Hyp |
Ref |
Expression |
1 |
|
cnfcom.s |
|
2 |
|
cnfcom.a |
|
3 |
|
cnfcom.b |
|
4 |
|
cnfcom.f |
|
5 |
|
cnfcom.g |
|
6 |
|
cnfcom.h |
|
7 |
|
cnfcom.t |
|
8 |
|
cnfcom.m |
|
9 |
|
cnfcom.k |
|
10 |
|
cnfcom.w |
|
11 |
|
cnfcom2.1 |
|
12 |
|
ovex |
|
13 |
5
|
oion |
|
14 |
12 13
|
ax-mp |
|
15 |
14
|
elexi |
|
16 |
15
|
uniex |
|
17 |
16
|
sucid |
|
18 |
1 2 3 4 5 6 7 8 9 10 11
|
cnfcom2lem |
|
19 |
17 18
|
eleqtrrid |
|
20 |
1 2 3 4 5 6 7 8 9 19
|
cnfcom |
|
21 |
10
|
oveq2i |
|
22 |
10
|
fveq2i |
|
23 |
21 22
|
oveq12i |
|
24 |
|
f1oeq3 |
|
25 |
23 24
|
ax-mp |
|
26 |
20 25
|
sylibr |
|
27 |
18
|
fveq2d |
|
28 |
|
f1oeq1 |
|
29 |
27 28
|
syl |
|
30 |
26 29
|
mpbird |
|
31 |
4
|
fveq2i |
|
32 |
|
omelon |
|
33 |
32
|
a1i |
|
34 |
1 33 2
|
cantnff1o |
|
35 |
|
f1ocnv |
|
36 |
|
f1of |
|
37 |
34 35 36
|
3syl |
|
38 |
37 3
|
ffvelrnd |
|
39 |
4 38
|
eqeltrid |
|
40 |
8
|
oveq1i |
|
41 |
40
|
a1i |
|
42 |
41
|
mpoeq3ia |
|
43 |
|
eqid |
|
44 |
|
seqomeq12 |
|
45 |
42 43 44
|
mp2an |
|
46 |
6 45
|
eqtri |
|
47 |
1 33 2 5 39 46
|
cantnfval |
|
48 |
31 47
|
syl5reqr |
|
49 |
18
|
fveq2d |
|
50 |
|
f1ocnvfv2 |
|
51 |
34 3 50
|
syl2anc |
|
52 |
48 49 51
|
3eqtr3d |
|
53 |
52
|
f1oeq2d |
|
54 |
30 53
|
mpbid |
|