Step |
Hyp |
Ref |
Expression |
1 |
|
simpl |
|
2 |
|
1oex |
|
3 |
|
djuex |
|
4 |
1 2 3
|
sylancl |
|
5 |
|
simpr |
|
6 |
|
df1o2 |
|
7 |
6
|
xpeq2i |
|
8 |
|
0ex |
|
9 |
2 8
|
xpsn |
|
10 |
7 9
|
eqtri |
|
11 |
|
ssun2 |
|
12 |
10 11
|
eqsstrri |
|
13 |
|
opex |
|
14 |
13
|
snss |
|
15 |
12 14
|
mpbir |
|
16 |
|
df-dju |
|
17 |
15 16
|
eleqtrri |
|
18 |
17
|
a1i |
|
19 |
|
difsnen |
|
20 |
4 5 18 19
|
syl3anc |
|
21 |
16
|
difeq1i |
|
22 |
|
xp01disjl |
|
23 |
|
disj3 |
|
24 |
22 23
|
mpbi |
|
25 |
|
difun2 |
|
26 |
10
|
difeq2i |
|
27 |
24 25 26
|
3eqtr2i |
|
28 |
21 27
|
eqtr4i |
|
29 |
|
xpsnen2g |
|
30 |
8 1 29
|
sylancr |
|
31 |
28 30
|
eqbrtrid |
|
32 |
|
entr |
|
33 |
20 31 32
|
syl2anc |
|