Step |
Hyp |
Ref |
Expression |
1 |
|
nfv |
|
2 |
|
nfmpt1 |
|
3 |
2
|
nfel1 |
|
4 |
1 3
|
nfan |
|
5 |
|
zex |
|
6 |
|
nn0ssz |
|
7 |
|
mapss |
|
8 |
5 6 7
|
mp2an |
|
9 |
8
|
sseli |
|
10 |
9
|
adantl |
|
11 |
|
mzpf |
|
12 |
|
mptfcl |
|
13 |
12
|
imp |
|
14 |
11 9 13
|
syl2an |
|
15 |
14
|
adantll |
|
16 |
|
eqid |
|
17 |
16
|
fvmpt2 |
|
18 |
10 15 17
|
syl2anc |
|
19 |
18
|
eqcomd |
|
20 |
19
|
eqeq1d |
|
21 |
20
|
ex |
|
22 |
4 21
|
ralrimi |
|
23 |
|
rabbi |
|
24 |
22 23
|
sylib |
|
25 |
|
nfcv |
|
26 |
|
nfcv |
|
27 |
|
nfv |
|
28 |
|
nffvmpt1 |
|
29 |
28
|
nfeq1 |
|
30 |
|
fveqeq2 |
|
31 |
25 26 27 29 30
|
cbvrabw |
|
32 |
24 31
|
eqtrdi |
|
33 |
|
df-rab |
|
34 |
32 33
|
eqtrdi |
|
35 |
|
elmapi |
|
36 |
|
ffn |
|
37 |
|
fnresdm |
|
38 |
35 36 37
|
3syl |
|
39 |
38
|
eqeq2d |
|
40 |
|
equcom |
|
41 |
39 40
|
syl6bb |
|
42 |
41
|
anbi1d |
|
43 |
42
|
rexbiia |
|
44 |
|
fveqeq2 |
|
45 |
44
|
ceqsrexbv |
|
46 |
43 45
|
bitr2i |
|
47 |
46
|
abbii |
|
48 |
34 47
|
eqtrdi |
|
49 |
|
simpl |
|
50 |
|
nn0z |
|
51 |
|
uzid |
|
52 |
50 51
|
syl |
|
53 |
52
|
adantr |
|
54 |
|
simpr |
|
55 |
|
eldioph |
|
56 |
49 53 54 55
|
syl3anc |
|
57 |
48 56
|
eqeltrd |
|