Step |
Hyp |
Ref |
Expression |
1 |
|
seqomlem.a |
|
2 |
|
frfnom |
|
3 |
1
|
reseq1i |
|
4 |
3
|
fneq1i |
|
5 |
2 4
|
mpbir |
|
6 |
|
fvres |
|
7 |
1
|
seqomlem1 |
|
8 |
6 7
|
eqtrd |
|
9 |
|
fvex |
|
10 |
|
opelxpi |
|
11 |
9 10
|
mpan2 |
|
12 |
8 11
|
eqeltrd |
|
13 |
12
|
rgen |
|
14 |
|
ffnfv |
|
15 |
5 13 14
|
mpbir2an |
|
16 |
|
frn |
|
17 |
15 16
|
ax-mp |
|
18 |
|
df-br |
|
19 |
|
fvelrnb |
|
20 |
5 19
|
ax-mp |
|
21 |
|
fvres |
|
22 |
21
|
eqeq1d |
|
23 |
22
|
rexbiia |
|
24 |
18 20 23
|
3bitri |
|
25 |
1
|
seqomlem1 |
|
26 |
25
|
adantl |
|
27 |
26
|
eqeq1d |
|
28 |
|
vex |
|
29 |
|
fvex |
|
30 |
28 29
|
opth1 |
|
31 |
27 30
|
syl6bi |
|
32 |
|
fveqeq2 |
|
33 |
32
|
biimpd |
|
34 |
31 33
|
syli |
|
35 |
|
fveq2 |
|
36 |
|
vex |
|
37 |
|
vex |
|
38 |
36 37
|
op2nd |
|
39 |
35 38
|
eqtr2di |
|
40 |
34 39
|
syl6 |
|
41 |
40
|
rexlimdva |
|
42 |
1
|
seqomlem1 |
|
43 |
|
fveqeq2 |
|
44 |
43
|
rspcev |
|
45 |
42 44
|
mpdan |
|
46 |
|
opeq2 |
|
47 |
46
|
eqeq2d |
|
48 |
47
|
rexbidv |
|
49 |
45 48
|
syl5ibrcom |
|
50 |
41 49
|
impbid |
|
51 |
24 50
|
syl5bb |
|
52 |
51
|
alrimiv |
|
53 |
|
fvex |
|
54 |
|
eqeq2 |
|
55 |
54
|
bibi2d |
|
56 |
55
|
albidv |
|
57 |
53 56
|
spcev |
|
58 |
52 57
|
syl |
|
59 |
|
eu6 |
|
60 |
58 59
|
sylibr |
|
61 |
60
|
rgen |
|
62 |
|
dff3 |
|
63 |
17 61 62
|
mpbir2an |
|
64 |
|
df-ima |
|
65 |
64
|
feq1i |
|
66 |
63 65
|
mpbir |
|
67 |
|
dffn2 |
|
68 |
66 67
|
mpbir |
|