Description: Consequence of trichotomy. (Contributed by NM, 14-May-1999)
Ref | Expression | ||
---|---|---|---|
Hypotheses | lt.1 | |- A e. RR |
|
lt.2 | |- B e. RR |
||
Assertion | letri3i | |- ( A = B <-> ( A <_ B /\ B <_ A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | lt.1 | |- A e. RR |
|
2 | lt.2 | |- B e. RR |
|
3 | letri3 | |- ( ( A e. RR /\ B e. RR ) -> ( A = B <-> ( A <_ B /\ B <_ A ) ) ) |
|
4 | 1 2 3 | mp2an | |- ( A = B <-> ( A <_ B /\ B <_ A ) ) |