Description: Subset relationship for intervals of extended reals. (Contributed by Mario Carneiro, 3-Nov-2013) (Revised by Mario Carneiro, 28-Apr-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | ixx.1 | |
|
ixxss2.2 | |
||
ixxss2.3 | |
||
Assertion | ixxss2 | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ixx.1 | |
|
2 | ixxss2.2 | |
|
3 | ixxss2.3 | |
|
4 | 2 | elixx3g | |
5 | 4 | simplbi | |
6 | 5 | adantl | |
7 | 6 | simp3d | |
8 | 4 | simprbi | |
9 | 8 | adantl | |
10 | 9 | simpld | |
11 | 9 | simprd | |
12 | simplr | |
|
13 | 6 | simp2d | |
14 | simpll | |
|
15 | 7 13 14 3 | syl3anc | |
16 | 11 12 15 | mp2and | |
17 | 6 | simp1d | |
18 | 1 | elixx1 | |
19 | 17 14 18 | syl2anc | |
20 | 7 10 16 19 | mpbir3and | |
21 | 20 | ex | |
22 | 21 | ssrdv | |