Step |
Hyp |
Ref |
Expression |
1 |
|
psgnval.g |
|
2 |
|
psgnval.t |
|
3 |
|
psgnval.n |
|
4 |
|
eqid |
|
5 |
1 3 4
|
psgneldm |
|
6 |
5
|
simplbi |
|
7 |
1 4
|
elbasfv |
|
8 |
6 7
|
syl |
|
9 |
1 2 3
|
psgneldm2 |
|
10 |
8 9
|
syl |
|
11 |
10
|
ibi |
|
12 |
|
simpr |
|
13 |
|
eqid |
|
14 |
|
ovex |
|
15 |
|
eqeq1 |
|
16 |
15
|
anbi2d |
|
17 |
14 16
|
spcev |
|
18 |
12 13 17
|
sylancl |
|
19 |
18
|
ex |
|
20 |
19
|
reximdva |
|
21 |
11 20
|
mpd |
|
22 |
|
rexcom4 |
|
23 |
21 22
|
sylib |
|
24 |
|
reeanv |
|
25 |
8
|
ad2antrr |
|
26 |
|
simplrl |
|
27 |
|
simplrr |
|
28 |
|
simprll |
|
29 |
|
simprrl |
|
30 |
28 29
|
eqtr3d |
|
31 |
1 2 25 26 27 30
|
psgnuni |
|
32 |
|
simprlr |
|
33 |
|
simprrr |
|
34 |
31 32 33
|
3eqtr4d |
|
35 |
34
|
ex |
|
36 |
35
|
rexlimdvva |
|
37 |
24 36
|
syl5bir |
|
38 |
37
|
alrimivv |
|
39 |
|
eqeq1 |
|
40 |
39
|
anbi2d |
|
41 |
40
|
rexbidv |
|
42 |
|
oveq2 |
|
43 |
42
|
eqeq2d |
|
44 |
|
fveq2 |
|
45 |
44
|
oveq2d |
|
46 |
45
|
eqeq2d |
|
47 |
43 46
|
anbi12d |
|
48 |
47
|
cbvrexvw |
|
49 |
41 48
|
bitrdi |
|
50 |
49
|
eu4 |
|
51 |
23 38 50
|
sylanbrc |
|