Description: In a Moore system, if a set is between another set and its closure, the two sets have the same closure. Deduction form. (Contributed by David Moews, 1-May-2017)
Ref | Expression | ||
---|---|---|---|
Hypotheses | mressmrcd.1 | |
|
mressmrcd.2 | |
||
mressmrcd.3 | |
||
mressmrcd.4 | |
||
Assertion | mressmrcd | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | mressmrcd.1 | |
|
2 | mressmrcd.2 | |
|
3 | mressmrcd.3 | |
|
4 | mressmrcd.4 | |
|
5 | 1 2 | mrcssvd | |
6 | 1 2 3 5 | mrcssd | |
7 | 3 5 | sstrd | |
8 | 4 7 | sstrd | |
9 | 1 2 8 | mrcidmd | |
10 | 6 9 | sseqtrd | |
11 | 1 2 4 7 | mrcssd | |
12 | 10 11 | eqssd | |