Step |
Hyp |
Ref |
Expression |
1 |
|
perpln.l |
|
2 |
|
perpln.1 |
|
3 |
|
perpln.2 |
|
4 |
|
df-perpg |
|
5 |
|
simpr |
|
6 |
5
|
fveq2d |
|
7 |
6 1
|
eqtr4di |
|
8 |
7
|
rneqd |
|
9 |
8
|
eleq2d |
|
10 |
8
|
eleq2d |
|
11 |
9 10
|
anbi12d |
|
12 |
5
|
fveq2d |
|
13 |
12
|
eleq2d |
|
14 |
13
|
ralbidv |
|
15 |
14
|
rexralbidv |
|
16 |
11 15
|
anbi12d |
|
17 |
16
|
opabbidv |
|
18 |
2
|
elexd |
|
19 |
1
|
fvexi |
|
20 |
|
rnexg |
|
21 |
19 20
|
mp1i |
|
22 |
21 21
|
xpexd |
|
23 |
|
opabssxp |
|
24 |
23
|
a1i |
|
25 |
22 24
|
ssexd |
|
26 |
4 17 18 25
|
fvmptd2 |
|
27 |
|
anass |
|
28 |
27
|
opabbii |
|
29 |
26 28
|
eqtrdi |
|
30 |
29
|
dmeqd |
|
31 |
|
dmopabss |
|
32 |
30 31
|
eqsstrdi |
|
33 |
|
relopabv |
|
34 |
26
|
releqd |
|
35 |
33 34
|
mpbiri |
|
36 |
|
brrelex12 |
|
37 |
35 3 36
|
syl2anc |
|
38 |
37
|
simpld |
|
39 |
37
|
simprd |
|
40 |
|
breldmg |
|
41 |
38 39 3 40
|
syl3anc |
|
42 |
32 41
|
sseldd |
|