Step |
Hyp |
Ref |
Expression |
1 |
|
f1o3d.1 |
|
2 |
|
f1o3d.2 |
|
3 |
|
f1o3d.3 |
|
4 |
|
f1o3d.4 |
|
5 |
2
|
ralrimiva |
|
6 |
|
eqid |
|
7 |
6
|
fnmpt |
|
8 |
5 7
|
syl |
|
9 |
1
|
fneq1d |
|
10 |
8 9
|
mpbird |
|
11 |
3
|
ralrimiva |
|
12 |
|
eqid |
|
13 |
12
|
fnmpt |
|
14 |
11 13
|
syl |
|
15 |
|
eleq1a |
|
16 |
2 15
|
syl |
|
17 |
16
|
impr |
|
18 |
4
|
biimpar |
|
19 |
18
|
exp42 |
|
20 |
19
|
com34 |
|
21 |
20
|
imp32 |
|
22 |
17 21
|
jcai |
|
23 |
|
eleq1a |
|
24 |
3 23
|
syl |
|
25 |
24
|
impr |
|
26 |
4
|
biimpa |
|
27 |
26
|
exp42 |
|
28 |
27
|
com23 |
|
29 |
28
|
com34 |
|
30 |
29
|
imp32 |
|
31 |
25 30
|
jcai |
|
32 |
22 31
|
impbida |
|
33 |
32
|
opabbidv |
|
34 |
|
df-mpt |
|
35 |
1 34
|
eqtrdi |
|
36 |
35
|
cnveqd |
|
37 |
|
cnvopab |
|
38 |
36 37
|
eqtrdi |
|
39 |
|
df-mpt |
|
40 |
39
|
a1i |
|
41 |
33 38 40
|
3eqtr4d |
|
42 |
41
|
fneq1d |
|
43 |
14 42
|
mpbird |
|
44 |
|
dff1o4 |
|
45 |
10 43 44
|
sylanbrc |
|
46 |
45 41
|
jca |
|