Answer
$min(a,min(b,c))=min(min(a,b),c)$
Work Step by Step
We are given the real numbers $a,b,c$.
Case 1: $min(a,min(b,c))=a$
$a\leq min(b,c)$
$a\leq b$ and $a\leq c$
$min(min(a,b),c)=min(a,c)=a$
So we got:
$min(a,min(b,c))=min(min(a,b),c)=a$
Case 2: $min(a,min(b,c))=b$
$min(b,c)\leq a$ and $min(b,c)=b$
$b\leq a$ and $b\leq c$
$min(min(a,b),c)=min(b,c)=b$
So we got:
$min(a,min(b,c))=min(min(a,b),c)=b$
Case 3: $min(a,min(b,c))=c$
$min(b,c)\leq a$ and $min(b,c)=c$
$c\leq a$ and $c\leq b$
$c\leq min(a,b)$
$min(min(a,b),c)=c$
So we got:
$min(a,min(b,c))=min(min(a,b),c)=c$
