Step |
Hyp |
Ref |
Expression |
1 |
|
preqsnd.1 |
|
2 |
|
preqsnd.2 |
|
3 |
1
|
adantl |
|
4 |
2
|
adantl |
|
5 |
|
simpl |
|
6 |
|
dfsn2 |
|
7 |
6
|
eqeq2i |
|
8 |
|
preq12bg |
|
9 |
|
oridm |
|
10 |
8 9
|
syl6bb |
|
11 |
7 10
|
syl5bb |
|
12 |
3 4 5 5 11
|
syl22anc |
|
13 |
|
snprc |
|
14 |
13
|
biimpi |
|
15 |
14
|
adantr |
|
16 |
15
|
eqeq2d |
|
17 |
|
prnzg |
|
18 |
|
eqneqall |
|
19 |
17 18
|
syl5com |
|
20 |
1 19
|
syl |
|
21 |
20
|
adantl |
|
22 |
16 21
|
sylbid |
|
23 |
|
eleq1 |
|
24 |
23
|
eqcoms |
|
25 |
24
|
notbid |
|
26 |
|
pm2.21 |
|
27 |
25 26
|
syl6bi |
|
28 |
27
|
com13 |
|
29 |
1 28
|
syl |
|
30 |
29
|
impcom |
|
31 |
30
|
impd |
|
32 |
22 31
|
impbid |
|
33 |
12 32
|
pm2.61ian |
|