Description: An interval is a subset of its closure. (Contributed by Paul Chapman, 18-Oct-2007) (Revised by Mario Carneiro, 3-Nov-2013)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ixx.1 | |
|
ixx.2 | |
||
ixx.3 | |
||
ixx.4 | |
||
Assertion | ixxssixx | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ixx.1 | |
|
2 | ixx.2 | |
|
3 | ixx.3 | |
|
4 | ixx.4 | |
|
5 | 1 | elmpocl | |
6 | simp1 | |
|
7 | 6 | a1i | |
8 | simpl | |
|
9 | 3simpa | |
|
10 | 3 | expimpd | |
11 | 8 9 10 | syl2im | |
12 | simpr | |
|
13 | 3simpb | |
|
14 | 4 | ancoms | |
15 | 14 | expimpd | |
16 | 12 13 15 | syl2im | |
17 | 7 11 16 | 3jcad | |
18 | 1 | elixx1 | |
19 | 2 | elixx1 | |
20 | 17 18 19 | 3imtr4d | |
21 | 5 20 | mpcom | |
22 | 21 | ssriv | |