Step |
Hyp |
Ref |
Expression |
1 |
|
aceq3lem.1 |
|
2 |
|
vex |
|
3 |
2
|
rnex |
|
4 |
3
|
pwex |
|
5 |
|
raleq |
|
6 |
5
|
exbidv |
|
7 |
4 6
|
spcv |
|
8 |
|
df-mpt |
|
9 |
1 8
|
eqtri |
|
10 |
|
vex |
|
11 |
10
|
eldm |
|
12 |
|
abn0 |
|
13 |
11 12
|
bitr4i |
|
14 |
|
vex |
|
15 |
10 14
|
brelrn |
|
16 |
15
|
abssi |
|
17 |
3 16
|
elpwi2 |
|
18 |
|
neeq1 |
|
19 |
|
fveq2 |
|
20 |
|
id |
|
21 |
19 20
|
eleq12d |
|
22 |
18 21
|
imbi12d |
|
23 |
22
|
rspcv |
|
24 |
17 23
|
ax-mp |
|
25 |
13 24
|
syl5bi |
|
26 |
25
|
imp |
|
27 |
|
fvex |
|
28 |
|
breq2 |
|
29 |
|
breq2 |
|
30 |
29
|
cbvabv |
|
31 |
27 28 30
|
elab2 |
|
32 |
26 31
|
sylib |
|
33 |
|
breq2 |
|
34 |
32 33
|
syl5ibrcom |
|
35 |
34
|
expimpd |
|
36 |
35
|
ssopab2dv |
|
37 |
|
opabss |
|
38 |
36 37
|
sstrdi |
|
39 |
9 38
|
eqsstrid |
|
40 |
27 1
|
fnmpti |
|
41 |
2
|
ssex |
|
42 |
41
|
adantr |
|
43 |
|
sseq1 |
|
44 |
|
fneq1 |
|
45 |
43 44
|
anbi12d |
|
46 |
45
|
spcegv |
|
47 |
42 46
|
mpcom |
|
48 |
39 40 47
|
sylancl |
|
49 |
48
|
exlimiv |
|
50 |
7 49
|
syl |
|
51 |
|
sseq1 |
|
52 |
|
fneq1 |
|
53 |
51 52
|
anbi12d |
|
54 |
53
|
cbvexvw |
|
55 |
50 54
|
sylib |
|