Step |
Hyp |
Ref |
Expression |
1 |
|
noinffv.1 |
|
2 |
|
iffalse |
|
3 |
1 2
|
syl5eq |
|
4 |
3
|
fveq1d |
|
5 |
4
|
3ad2ant1 |
|
6 |
|
dmeq |
|
7 |
6
|
eleq2d |
|
8 |
|
breq1 |
|
9 |
8
|
notbid |
|
10 |
|
reseq1 |
|
11 |
10
|
eqeq1d |
|
12 |
9 11
|
imbi12d |
|
13 |
12
|
ralbidv |
|
14 |
7 13
|
anbi12d |
|
15 |
14
|
rspcev |
|
16 |
15
|
3impb |
|
17 |
16
|
3ad2ant3 |
|
18 |
|
simp32 |
|
19 |
|
eleq1 |
|
20 |
|
suceq |
|
21 |
20
|
reseq2d |
|
22 |
20
|
reseq2d |
|
23 |
21 22
|
eqeq12d |
|
24 |
23
|
imbi2d |
|
25 |
24
|
ralbidv |
|
26 |
19 25
|
anbi12d |
|
27 |
26
|
rexbidv |
|
28 |
27
|
elabg |
|
29 |
18 28
|
syl |
|
30 |
17 29
|
mpbird |
|
31 |
|
eleq1 |
|
32 |
|
suceq |
|
33 |
32
|
reseq2d |
|
34 |
32
|
reseq2d |
|
35 |
33 34
|
eqeq12d |
|
36 |
35
|
imbi2d |
|
37 |
36
|
ralbidv |
|
38 |
|
fveqeq2 |
|
39 |
31 37 38
|
3anbi123d |
|
40 |
39
|
rexbidv |
|
41 |
40
|
iotabidv |
|
42 |
|
eqid |
|
43 |
|
iotaex |
|
44 |
41 42 43
|
fvmpt |
|
45 |
30 44
|
syl |
|
46 |
|
simp1 |
|
47 |
|
simp2 |
|
48 |
|
simp3 |
|
49 |
|
eqidd |
|
50 |
|
fveq1 |
|
51 |
50
|
eqeq1d |
|
52 |
7 13 51
|
3anbi123d |
|
53 |
52
|
rspcev |
|
54 |
46 47 48 49 53
|
syl13anc |
|
55 |
54
|
3ad2ant3 |
|
56 |
|
fvex |
|
57 |
|
eqid |
|
58 |
|
fvex |
|
59 |
|
eqeq2 |
|
60 |
59
|
3anbi3d |
|
61 |
58 60
|
spcev |
|
62 |
57 61
|
mp3an3 |
|
63 |
62
|
reximi |
|
64 |
|
rexcom4 |
|
65 |
63 64
|
sylib |
|
66 |
16 65
|
syl |
|
67 |
66
|
3ad2ant3 |
|
68 |
|
simp2l |
|
69 |
|
noinfprefixmo |
|
70 |
68 69
|
syl |
|
71 |
|
df-eu |
|
72 |
67 70 71
|
sylanbrc |
|
73 |
|
eqeq2 |
|
74 |
73
|
3anbi3d |
|
75 |
74
|
rexbidv |
|
76 |
75
|
iota2 |
|
77 |
56 72 76
|
sylancr |
|
78 |
55 77
|
mpbid |
|
79 |
5 45 78
|
3eqtrd |
|