Step |
Hyp |
Ref |
Expression |
1 |
|
sursubmefmnd.m |
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2 |
|
vex |
|
3 |
|
foeq1 |
|
4 |
2 3
|
elab |
|
5 |
|
fof |
|
6 |
|
eqid |
|
7 |
1 6
|
elefmndbas |
|
8 |
5 7
|
syl5ibr |
|
9 |
4 8
|
syl5bi |
|
10 |
9
|
ssrdv |
|
11 |
1
|
efmndid |
|
12 |
|
resiexg |
|
13 |
|
f1oi |
|
14 |
|
f1ofo |
|
15 |
13 14
|
mp1i |
|
16 |
|
foeq1 |
|
17 |
12 15 16
|
elabd |
|
18 |
11 17
|
eqeltrrd |
|
19 |
|
vex |
|
20 |
|
foeq1 |
|
21 |
19 20
|
elab |
|
22 |
4 21
|
anbi12i |
|
23 |
|
foco |
|
24 |
23
|
adantl |
|
25 |
|
fof |
|
26 |
5 25
|
anim12i |
|
27 |
1 6
|
elefmndbas |
|
28 |
7 27
|
anbi12d |
|
29 |
26 28
|
syl5ibr |
|
30 |
29
|
imp |
|
31 |
|
eqid |
|
32 |
1 6 31
|
efmndov |
|
33 |
30 32
|
syl |
|
34 |
33
|
eleq1d |
|
35 |
2 19
|
coex |
|
36 |
|
foeq1 |
|
37 |
35 36
|
elab |
|
38 |
34 37
|
bitrdi |
|
39 |
24 38
|
mpbird |
|
40 |
39
|
ex |
|
41 |
22 40
|
syl5bi |
|
42 |
41
|
ralrimivv |
|
43 |
1
|
efmndmnd |
|
44 |
|
eqid |
|
45 |
6 44 31
|
issubm |
|
46 |
43 45
|
syl |
|
47 |
10 18 42 46
|
mpbir3and |
|