How can I show that the limit of the following function when the variables {x,y} tend to zero, is zero? Mathematica gives the error "{x,y} is not a valid variable". Domains are $0<x<10$ and $0<y<1$.

Cosh[1/Sqrt[y]] Sinh[x/Sqrt[y]] - y Cosh[x/Sqrt[y]]

Limit[Cosh[1/Sqrt[y]] Sinh[x/Sqrt[y]] - 
  y Cosh[x/Sqrt[y]], {x, y} -> {0, 0}]

Any comment is welcome.