Step |
Hyp |
Ref |
Expression |
1 |
|
frege129d.f |
|
2 |
|
frege129d.a |
|
3 |
|
frege129d.c |
|
4 |
|
frege129d.or |
|
5 |
|
frege129d.fun |
|
6 |
1
|
adantr |
|
7 |
2
|
adantr |
|
8 |
3
|
adantr |
|
9 |
|
simpr |
|
10 |
5
|
adantr |
|
11 |
6 7 8 9 10
|
frege126d |
|
12 |
|
biid |
|
13 |
|
eqcom |
|
14 |
|
biid |
|
15 |
12 13 14
|
3orbi123i |
|
16 |
11 15
|
sylib |
|
17 |
|
3orcomb |
|
18 |
|
3orrot |
|
19 |
17 18
|
sylbb |
|
20 |
16 19
|
syl |
|
21 |
20
|
ex |
|
22 |
|
simpr |
|
23 |
3
|
eqcomd |
|
24 |
|
funbrfvb |
|
25 |
24
|
biimpd |
|
26 |
5 2 25
|
syl2anc |
|
27 |
23 26
|
mpd |
|
28 |
1 27
|
frege91d |
|
29 |
28
|
adantr |
|
30 |
22 29
|
eqbrtrrd |
|
31 |
30
|
ex |
|
32 |
|
3mix1 |
|
33 |
31 32
|
syl6 |
|
34 |
1
|
adantr |
|
35 |
|
funrel |
|
36 |
5 35
|
syl |
|
37 |
|
reltrclfv |
|
38 |
1 36 37
|
syl2anc |
|
39 |
|
brrelex1 |
|
40 |
38 39
|
sylan |
|
41 |
|
fvex |
|
42 |
3 41
|
eqeltrdi |
|
43 |
42
|
adantr |
|
44 |
2
|
elexd |
|
45 |
44
|
adantr |
|
46 |
|
simpr |
|
47 |
27
|
adantr |
|
48 |
34 40 43 45 46 47
|
frege96d |
|
49 |
48
|
ex |
|
50 |
49 32
|
syl6 |
|
51 |
21 33 50
|
3jaod |
|
52 |
4 51
|
mpd |
|