Step |
Hyp |
Ref |
Expression |
1 |
|
fsuppunbi.u |
|
2 |
|
relfsupp |
|
3 |
2
|
brrelex12i |
|
4 |
|
unexb |
|
5 |
|
simpr |
|
6 |
5
|
adantr |
|
7 |
|
simprlr |
|
8 |
7
|
suppun |
|
9 |
6 8
|
ssfid |
|
10 |
|
fununfun |
|
11 |
10
|
simpld |
|
12 |
11
|
adantr |
|
13 |
12
|
adantr |
|
14 |
|
simprll |
|
15 |
|
simpr |
|
16 |
15
|
adantl |
|
17 |
|
funisfsupp |
|
18 |
13 14 16 17
|
syl3anc |
|
19 |
9 18
|
mpbird |
|
20 |
|
uncom |
|
21 |
20
|
oveq1i |
|
22 |
21
|
eleq1i |
|
23 |
22
|
biimpi |
|
24 |
23
|
adantl |
|
25 |
24
|
adantr |
|
26 |
14
|
suppun |
|
27 |
25 26
|
ssfid |
|
28 |
10
|
simprd |
|
29 |
28
|
adantr |
|
30 |
29
|
adantr |
|
31 |
|
funisfsupp |
|
32 |
30 7 16 31
|
syl3anc |
|
33 |
27 32
|
mpbird |
|
34 |
19 33
|
jca |
|
35 |
34
|
a1d |
|
36 |
35
|
ex |
|
37 |
|
fsuppimp |
|
38 |
36 37
|
syl11 |
|
39 |
4 38
|
sylanbr |
|
40 |
3 39
|
mpcom |
|
41 |
40
|
com12 |
|
42 |
|
simpl |
|
43 |
|
simpr |
|
44 |
42 43
|
fsuppun |
|
45 |
44
|
adantl |
|
46 |
1
|
adantr |
|
47 |
2
|
brrelex1i |
|
48 |
2
|
brrelex1i |
|
49 |
|
unexg |
|
50 |
47 48 49
|
syl2an |
|
51 |
50
|
adantl |
|
52 |
2
|
brrelex2i |
|
53 |
52
|
adantr |
|
54 |
53
|
adantl |
|
55 |
|
funisfsupp |
|
56 |
46 51 54 55
|
syl3anc |
|
57 |
45 56
|
mpbird |
|
58 |
57
|
ex |
|
59 |
41 58
|
impbid |
|