Description: A number is less than or equal to the maximum of it and another. (Contributed by NM, 3-Apr-2005)
Ref | Expression | ||
---|---|---|---|
Assertion | max2 | |- ( ( A e. RR /\ B e. RR ) -> B <_ if ( A <_ B , B , A ) ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | rexr | |- ( A e. RR -> A e. RR* ) |
|
2 | rexr | |- ( B e. RR -> B e. RR* ) |
|
3 | xrmax2 | |- ( ( A e. RR* /\ B e. RR* ) -> B <_ if ( A <_ B , B , A ) ) |
|
4 | 1 2 3 | syl2an | |- ( ( A e. RR /\ B e. RR ) -> B <_ if ( A <_ B , B , A ) ) |