Step |
Hyp |
Ref |
Expression |
1 |
|
ssmapsn.f |
|
2 |
|
ssmapsn.a |
|
3 |
|
ssmapsn.c |
|
4 |
|
ssmapsn.d |
|
5 |
3
|
sselda |
|
6 |
|
elmapi |
|
7 |
5 6
|
syl |
|
8 |
7
|
ffnd |
|
9 |
4
|
a1i |
|
10 |
|
ovexd |
|
11 |
10 3
|
ssexd |
|
12 |
|
rnexg |
|
13 |
12
|
rgen |
|
14 |
|
iunexg |
|
15 |
11 13 14
|
sylancl |
|
16 |
9 15
|
eqeltrd |
|
17 |
16
|
adantr |
|
18 |
|
ssiun2 |
|
19 |
18
|
adantl |
|
20 |
|
snidg |
|
21 |
2 20
|
syl |
|
22 |
21
|
adantr |
|
23 |
8 22
|
fnfvelrnd |
|
24 |
19 23
|
sseldd |
|
25 |
24 4
|
eleqtrrdi |
|
26 |
8 17 25
|
elmapsnd |
|
27 |
16
|
adantr |
|
28 |
|
snex |
|
29 |
28
|
a1i |
|
30 |
|
simpr |
|
31 |
21
|
adantr |
|
32 |
27 29 30 31
|
fvmap |
|
33 |
|
rneq |
|
34 |
33
|
cbviunv |
|
35 |
4 34
|
eqtri |
|
36 |
32 35
|
eleqtrdi |
|
37 |
|
eliun |
|
38 |
36 37
|
sylib |
|
39 |
|
simp3 |
|
40 |
|
simp1l |
|
41 |
40 2
|
syl |
|
42 |
|
eqid |
|
43 |
|
simp1r |
|
44 |
|
elmapfn |
|
45 |
43 44
|
syl |
|
46 |
3
|
sselda |
|
47 |
|
elmapfn |
|
48 |
46 47
|
syl |
|
49 |
48
|
3adant3 |
|
50 |
49
|
3adant1r |
|
51 |
41 42 45 50
|
fsneqrn |
|
52 |
39 51
|
mpbird |
|
53 |
|
simp2 |
|
54 |
52 53
|
eqeltrd |
|
55 |
54
|
rexlimdv3a |
|
56 |
38 55
|
mpd |
|
57 |
26 56
|
impbida |
|
58 |
57
|
alrimiv |
|
59 |
|
nfcv |
|
60 |
|
nfcv |
|
61 |
|
nfcv |
|
62 |
1 60 61
|
nfov |
|
63 |
59 62
|
cleqf |
|
64 |
58 63
|
sylibr |
|