Step |
Hyp |
Ref |
Expression |
1 |
|
simpr |
|
2 |
|
simpl |
|
3 |
|
eqid |
|
4 |
3
|
neiss2 |
|
5 |
3
|
neii1 |
|
6 |
3
|
neiint |
|
7 |
2 4 5 6
|
syl3anc |
|
8 |
1 7
|
mpbid |
|
9 |
|
ssinss1 |
|
10 |
8 9
|
syl |
|
11 |
10
|
3adant3 |
|
12 |
|
inss2 |
|
13 |
|
simpr |
|
14 |
|
simpl |
|
15 |
3
|
neiss2 |
|
16 |
3
|
neii1 |
|
17 |
3
|
neiint |
|
18 |
14 15 16 17
|
syl3anc |
|
19 |
13 18
|
mpbid |
|
20 |
19
|
3adant2 |
|
21 |
12 20
|
sstrid |
|
22 |
11 21
|
ssind |
|
23 |
|
simp1 |
|
24 |
5
|
3adant3 |
|
25 |
16
|
3adant2 |
|
26 |
3
|
ntrin |
|
27 |
23 24 25 26
|
syl3anc |
|
28 |
22 27
|
sseqtrrd |
|
29 |
|
ssinss1 |
|
30 |
4 29
|
syl |
|
31 |
|
ssinss1 |
|
32 |
5 31
|
syl |
|
33 |
3
|
neiint |
|
34 |
2 30 32 33
|
syl3anc |
|
35 |
34
|
3adant3 |
|
36 |
28 35
|
mpbird |
|