Step |
Hyp |
Ref |
Expression |
1 |
|
df-s4 |
|
2 |
|
simpl |
|
3 |
2
|
adantr |
|
4 |
|
simpr |
|
5 |
4
|
adantr |
|
6 |
|
simpl |
|
7 |
6
|
adantl |
|
8 |
3 5 7
|
s3cld |
|
9 |
|
simpr |
|
10 |
9
|
adantl |
|
11 |
|
cats1un |
|
12 |
8 10 11
|
syl2anc |
|
13 |
|
df-s3 |
|
14 |
|
s2cl |
|
15 |
14
|
adantr |
|
16 |
|
cats1un |
|
17 |
15 7 16
|
syl2anc |
|
18 |
13 17
|
syl5eq |
|
19 |
|
s2prop |
|
20 |
19
|
adantr |
|
21 |
20
|
uneq1d |
|
22 |
18 21
|
eqtrd |
|
23 |
22
|
uneq1d |
|
24 |
12 23
|
eqtrd |
|
25 |
|
unass |
|
26 |
25
|
a1i |
|
27 |
|
df-pr |
|
28 |
|
s2len |
|
29 |
28
|
a1i |
|
30 |
29
|
opeq1d |
|
31 |
|
s3len |
|
32 |
31
|
a1i |
|
33 |
32
|
opeq1d |
|
34 |
30 33
|
preq12d |
|
35 |
27 34
|
syl5eqr |
|
36 |
35
|
uneq2d |
|
37 |
24 26 36
|
3eqtrd |
|
38 |
1 37
|
syl5eq |
|