Step |
Hyp |
Ref |
Expression |
1 |
|
elpri |
|
2 |
|
eleq1 |
|
3 |
|
simprrr |
|
4 |
|
necom |
|
5 |
|
neeq2 |
|
6 |
5
|
eqcoms |
|
7 |
6
|
biimpcd |
|
8 |
4 7
|
sylbi |
|
9 |
8
|
adantr |
|
10 |
9
|
impcom |
|
11 |
3 10
|
eldifsnd |
|
12 |
|
prid2g |
|
13 |
12
|
adantl |
|
14 |
13
|
ad2antll |
|
15 |
2 11 14
|
rspcedvdw |
|
16 |
15
|
ex |
|
17 |
|
eleq1 |
|
18 |
|
simprrl |
|
19 |
|
neeq2 |
|
20 |
19
|
eqcoms |
|
21 |
20
|
biimpcd |
|
22 |
21
|
adantr |
|
23 |
22
|
impcom |
|
24 |
18 23
|
eldifsnd |
|
25 |
|
prid1g |
|
26 |
25
|
adantr |
|
27 |
26
|
ad2antll |
|
28 |
17 24 27
|
rspcedvdw |
|
29 |
28
|
ex |
|
30 |
16 29
|
jaoi |
|
31 |
1 30
|
syl |
|
32 |
31
|
3impib |
|