An exercise in Elementary Algebra

Question

Prove (logically) that: If ($x\ge a \implies x\ge b$) then $a\ge b$.

($x$ positive and unknown and $a,b\in\mathbb N^+$).

Answer 1

If the implication is true for every $x$, it's particularity true for $x=a$.

Apply it to the logical sentence and get the desired result.

Answer 2

$X >= B$ if and only if $X >= A$. This means that if $X >= A$ would mean $X >=B$. So it definitely holds true that $A >= B$.