Step |
Hyp |
Ref |
Expression |
1 |
|
pssss |
|
2 |
|
dmss |
|
3 |
1 2
|
syl |
|
4 |
3
|
a1i |
|
5 |
|
pssdif |
|
6 |
|
n0 |
|
7 |
5 6
|
sylib |
|
8 |
7
|
adantl |
|
9 |
|
funrel |
|
10 |
|
reldif |
|
11 |
9 10
|
syl |
|
12 |
|
elrel |
|
13 |
|
eleq1 |
|
14 |
|
df-br |
|
15 |
13 14
|
bitr4di |
|
16 |
15
|
biimpcd |
|
17 |
16
|
adantl |
|
18 |
17
|
2eximdv |
|
19 |
12 18
|
mpd |
|
20 |
19
|
ex |
|
21 |
11 20
|
syl |
|
22 |
21
|
adantr |
|
23 |
|
difss |
|
24 |
23
|
ssbri |
|
25 |
24
|
eximi |
|
26 |
25
|
a1i |
|
27 |
|
brdif |
|
28 |
27
|
simprbi |
|
29 |
28
|
adantl |
|
30 |
1
|
ssbrd |
|
31 |
30
|
ad2antlr |
|
32 |
|
dffun2 |
|
33 |
32
|
simprbi |
|
34 |
|
2sp |
|
35 |
34
|
sps |
|
36 |
33 35
|
syl |
|
37 |
|
breq2 |
|
38 |
37
|
biimprd |
|
39 |
36 38
|
syl6 |
|
40 |
39
|
expd |
|
41 |
27
|
simplbi |
|
42 |
40 41
|
impel |
|
43 |
42
|
adantlr |
|
44 |
43
|
com23 |
|
45 |
31 44
|
mpdd |
|
46 |
45
|
exlimdv |
|
47 |
29 46
|
mtod |
|
48 |
47
|
ex |
|
49 |
48
|
exlimdv |
|
50 |
26 49
|
jcad |
|
51 |
50
|
eximdv |
|
52 |
22 51
|
syld |
|
53 |
52
|
exlimdv |
|
54 |
8 53
|
mpd |
|
55 |
|
nss |
|
56 |
|
vex |
|
57 |
56
|
eldm |
|
58 |
56
|
eldm |
|
59 |
58
|
notbii |
|
60 |
57 59
|
anbi12i |
|
61 |
60
|
exbii |
|
62 |
55 61
|
bitri |
|
63 |
54 62
|
sylibr |
|
64 |
63
|
ex |
|
65 |
4 64
|
jcad |
|
66 |
|
dfpss3 |
|
67 |
65 66
|
syl6ibr |
|