Description: Separated sets are disjoint. Note that in general separatedness also requires T C_ U. J and ( S i^i ( ( clsJ )T ) ) = (/) as well but they are unnecessary here. (Contributed by Zhi Wang, 7-Sep-2024)
Ref | Expression | ||
---|---|---|---|
Hypotheses | sepdisj.1 | ||
sepdisj.2 | |||
sepdisj.3 | |||
Assertion | sepdisj |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sepdisj.1 | ||
2 | sepdisj.2 | ||
3 | sepdisj.3 | ||
4 | eqid | ||
5 | 4 | sscls | |
6 | 1 2 5 | syl2anc | |
7 | 6 3 | ssdisjd |