There is a theorem (I can't remember its name) saying that for any irrational number $x$ and any $0<a<b<1$, there exists a positive integer $n$ such that $\{nx\}\in (a,b)$, where $\{\cdot\}$ denotes the fractional part.

Is it true that for any irrational numbers $x,y$ and any $0<a<b<1,0<c<d<1$, there exists a positive integer $n$ such that $\{nx\}\in (a,b)$ and $\{ny\}\in (c,d)$? Is there a theorem for this, or is it simple to prove?