Step |
Hyp |
Ref |
Expression |
1 |
|
domnsym |
|
2 |
|
simp3 |
|
3 |
|
infdif |
|
4 |
3
|
ensymd |
|
5 |
|
sdomentr |
|
6 |
2 4 5
|
syl2anc |
|
7 |
1 6
|
nsyl3 |
|
8 |
7
|
3expia |
|
9 |
8
|
3adant2 |
|
10 |
9
|
con2d |
|
11 |
|
domtri2 |
|
12 |
11
|
3adant3 |
|
13 |
10 12
|
sylibrd |
|
14 |
|
simp1 |
|
15 |
|
difss |
|
16 |
|
ssdomg |
|
17 |
14 15 16
|
mpisyl |
|
18 |
|
domtr |
|
19 |
18
|
ex |
|
20 |
17 19
|
syl |
|
21 |
13 20
|
impbid |
|