Description: Conditions for a collection of sets A ( a ) for a e. V to be disjoint. (Contributed by AV, 9-Jan-2022)
Ref | Expression | ||
---|---|---|---|
Hypotheses | disjord.1 | |
|
disjord.2 | |
||
Assertion | disjord | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | disjord.1 | |
|
2 | disjord.2 | |
|
3 | orc | |
|
4 | 3 | a1d | |
5 | 2 | 3expia | |
6 | 5 | con3d | |
7 | 6 | impancom | |
8 | 7 | ralrimiv | |
9 | disj | |
|
10 | 8 9 | sylibr | |
11 | 10 | olcd | |
12 | 11 | expcom | |
13 | 4 12 | pm2.61i | |
14 | 13 | adantr | |
15 | 14 | ralrimivva | |
16 | 1 | disjor | |
17 | 15 16 | sylibr | |