| 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 |
|