Show that Xn->0 (in probability) iff |Xn|->0 (in probability).

What i have so far

|Xn|->0 (in probability) iff for any ε>0 P(||Xn|-ε|>=0)->0 as n->inf. But P(||Xn|-ε|>=0)=P(|Xn|>=ε)=P(|Xn|>=0)=P(|Xn-ε|>=ε) so this is true iff Xn->0 (in probability)

Is this logic correct?