Step |
Hyp |
Ref |
Expression |
1 |
|
brprop.a |
|
2 |
|
brprop.b |
|
3 |
|
brprop.c |
|
4 |
|
brprop.d |
|
5 |
|
mptprop.1 |
|
6 |
|
coprprop.e |
|
7 |
|
coprprop.f |
|
8 |
|
coprprop.1 |
|
9 |
|
coundir |
|
10 |
1 2 6
|
cosnop |
|
11 |
5
|
necomd |
|
12 |
4 6 11
|
cosnopne |
|
13 |
10 12
|
uneq12d |
|
14 |
|
un0 |
|
15 |
13 14
|
eqtrdi |
|
16 |
9 15
|
syl5eq |
|
17 |
|
coundir |
|
18 |
2 7 5
|
cosnopne |
|
19 |
3 4 7
|
cosnop |
|
20 |
18 19
|
uneq12d |
|
21 |
|
0un |
|
22 |
20 21
|
eqtrdi |
|
23 |
17 22
|
syl5eq |
|
24 |
16 23
|
uneq12d |
|
25 |
|
df-pr |
|
26 |
|
df-pr |
|
27 |
25 26
|
coeq12i |
|
28 |
|
coundi |
|
29 |
27 28
|
eqtri |
|
30 |
|
df-pr |
|
31 |
24 29 30
|
3eqtr4g |
|