Description: Transitive law for ordering on extended reals. (Contributed by Mario Carneiro, 23-Aug-2015)
Ref | Expression | ||
---|---|---|---|
Hypotheses | xrlttrd.1 | |
|
xrlttrd.2 | |
||
xrlttrd.3 | |
||
xrletrd.4 | |
||
xrletrd.5 | |
||
Assertion | xrletrd | |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xrlttrd.1 | |
|
2 | xrlttrd.2 | |
|
3 | xrlttrd.3 | |
|
4 | xrletrd.4 | |
|
5 | xrletrd.5 | |
|
6 | xrletr | |
|
7 | 1 2 3 6 | syl3anc | |
8 | 4 5 7 | mp2and | |