Description: A strict order relation is a transitive relation. (Contributed by NM, 10-Feb-1996) (Revised by Mario Carneiro, 10-May-2013)
Ref | Expression | ||
---|---|---|---|
Hypotheses | soi.1 | |
|
soi.2 | |
||
Assertion | sotri | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | soi.1 | |
|
2 | soi.2 | |
|
3 | 2 | brel | |
4 | 3 | simpld | |
5 | 2 | brel | |
6 | 4 5 | anim12i | |
7 | sotr | |
|
8 | 1 7 | mpan | |
9 | 8 | 3expb | |
10 | 6 9 | mpcom | |