Step |
Hyp |
Ref |
Expression |
1 |
|
madeval |
|
2 |
|
scutcut |
|
3 |
2
|
simp1d |
|
4 |
|
eleq1 |
|
5 |
4
|
biimpd |
|
6 |
3 5
|
mpan9 |
|
7 |
6
|
rexlimivw |
|
8 |
7
|
rexlimivw |
|
9 |
8
|
pm4.71ri |
|
10 |
9
|
abbii |
|
11 |
|
eleq1 |
|
12 |
|
breq1 |
|
13 |
11 12
|
anbi12d |
|
14 |
13
|
rexxp |
|
15 |
|
imaindm |
|
16 |
|
dmscut |
|
17 |
16
|
ineq2i |
|
18 |
17
|
imaeq2i |
|
19 |
15 18
|
eqtri |
|
20 |
19
|
eleq2i |
|
21 |
|
vex |
|
22 |
21
|
elima |
|
23 |
|
elin |
|
24 |
23
|
anbi1i |
|
25 |
|
anass |
|
26 |
24 25
|
bitri |
|
27 |
26
|
rexbii2 |
|
28 |
20 22 27
|
3bitri |
|
29 |
|
df-br |
|
30 |
29
|
anbi1i |
|
31 |
|
df-ov |
|
32 |
31
|
eqeq1i |
|
33 |
|
scutf |
|
34 |
|
ffn |
|
35 |
33 34
|
ax-mp |
|
36 |
|
fnbrfvb |
|
37 |
35 36
|
mpan |
|
38 |
32 37
|
syl5bb |
|
39 |
38
|
pm5.32i |
|
40 |
30 39
|
bitri |
|
41 |
40
|
2rexbii |
|
42 |
14 28 41
|
3bitr4i |
|
43 |
42
|
abbi2i |
|
44 |
|
df-rab |
|
45 |
10 43 44
|
3eqtr4i |
|
46 |
1 45
|
eqtrdi |
|