Description: The minimum of two numbers is less than or equal to the second. (Contributed by Glauco Siliprandi, 5-Feb-2022)
Ref | Expression | ||
---|---|---|---|
Hypotheses | min2d.1 | |- ( ph -> A e. RR ) |
|
min2d.2 | |- ( ph -> B e. RR ) |
||
Assertion | min2d | |- ( ph -> if ( A <_ B , A , B ) <_ B ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | min2d.1 | |- ( ph -> A e. RR ) |
|
2 | min2d.2 | |- ( ph -> B e. RR ) |
|
3 | min2 | |- ( ( A e. RR /\ B e. RR ) -> if ( A <_ B , A , B ) <_ B ) |
|
4 | 1 2 3 | syl2anc | |- ( ph -> if ( A <_ B , A , B ) <_ B ) |