Step |
Hyp |
Ref |
Expression |
1 |
|
preq12nebg |
|
2 |
|
prid1g |
|
3 |
2
|
3ad2ant1 |
|
4 |
3
|
adantr |
|
5 |
|
preq1 |
|
6 |
5
|
adantl |
|
7 |
4 6
|
eleqtrd |
|
8 |
7
|
ex |
|
9 |
|
prid2g |
|
10 |
9
|
3ad2ant2 |
|
11 |
|
preq2 |
|
12 |
11
|
eleq2d |
|
13 |
10 12
|
syl5ibcom |
|
14 |
8 13
|
anim12d |
|
15 |
|
prid2g |
|
16 |
15
|
3ad2ant1 |
|
17 |
|
preq2 |
|
18 |
17
|
eleq2d |
|
19 |
16 18
|
syl5ibcom |
|
20 |
|
prid1g |
|
21 |
20
|
3ad2ant2 |
|
22 |
|
preq1 |
|
23 |
22
|
eleq2d |
|
24 |
21 23
|
syl5ibcom |
|
25 |
19 24
|
anim12d |
|
26 |
14 25
|
jaod |
|
27 |
|
elprg |
|
28 |
27
|
3ad2ant1 |
|
29 |
|
elprg |
|
30 |
29
|
3ad2ant2 |
|
31 |
28 30
|
anbi12d |
|
32 |
|
eqtr3 |
|
33 |
|
eqneqall |
|
34 |
32 33
|
syl |
|
35 |
|
olc |
|
36 |
35
|
a1d |
|
37 |
|
orc |
|
38 |
37
|
a1d |
|
39 |
|
eqtr3 |
|
40 |
39 33
|
syl |
|
41 |
34 36 38 40
|
ccase |
|
42 |
41
|
com12 |
|
43 |
42
|
3ad2ant3 |
|
44 |
31 43
|
sylbid |
|
45 |
26 44
|
impbid |
|
46 |
1 45
|
bitrd |
|